Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(-3(5x-\frac{4}{5})=-8x+\frac{2}{11}\)
2. \(-5(-3x+\frac{4}{3})=7x+\frac{6}{11}\)
3. \(-3(-5x+\frac{2}{7})=2x+\frac{9}{11}\)
4. \(4(-5x+\frac{4}{9})=-3x+\frac{2}{5}\)
5. \(-6(5x-\frac{2}{5})=7x+\frac{8}{9}\)
6. \(5(-4x-\frac{5}{2})=-7x+\frac{6}{5}\)
7. \(-6(2x+\frac{5}{11})=-5x+\frac{10}{7}\)
8. \(-6(5x+\frac{3}{11})=-7x+\frac{4}{7}\)
9. \(-7(4x-\frac{2}{5})=8x+\frac{10}{7}\)
10. \(-5(-5x+\frac{3}{8})=-9x+\frac{4}{11}\)
11. \(-3(2x+\frac{2}{7})=-7x+\frac{5}{7}\)
12. \(-6(4x+\frac{5}{7})=-5x+\frac{8}{9}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+132} & = & \color{red}{-440x} +10 \\\Leftrightarrow & -825x \color{red}{+132} \color{blue}{-132} \color{blue}{+440x} & = & \color{red}{-440x} +10 \color{blue}{+440x} \color{blue}{-132} \\\Leftrightarrow & -825x+440x& = & 10-132 \\\Leftrightarrow & \color{red}{-385} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-385} & & \\\Leftrightarrow & x = \frac{122}{385} & & \\ & V = \left\{ \frac{122}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-220} & = & \color{red}{231x} +18 \\\Leftrightarrow & 495x \color{red}{-220} \color{blue}{+220} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{+220} \\\Leftrightarrow & 495x-231x& = & 18+220 \\\Leftrightarrow & \color{red}{264} x& = & 238 \\\Leftrightarrow & x = \frac{238}{264} & & \\\Leftrightarrow & x = \frac{119}{132} & & \\ & V = \left\{ \frac{119}{132} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 2x+\frac{9}{11} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 2x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-66} & = & \color{red}{154x} +63 \\\Leftrightarrow & 1155x \color{red}{-66} \color{blue}{+66} \color{blue}{-154x} & = & \color{red}{154x} +63 \color{blue}{-154x} \color{blue}{+66} \\\Leftrightarrow & 1155x-154x& = & 63+66 \\\Leftrightarrow & \color{red}{1001} x& = & 129 \\\Leftrightarrow & x = \frac{129}{1001} & & \\ & V = \left\{ \frac{129}{1001} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{9})& = & -3x+\frac{2}{5} \\\Leftrightarrow & -20x+\frac{16}{9}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x+ \frac{80}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{+80} & = & \color{red}{-135x} +18 \\\Leftrightarrow & -900x \color{red}{+80} \color{blue}{-80} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{-80} \\\Leftrightarrow & -900x+135x& = & 18-80 \\\Leftrightarrow & \color{red}{-765} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-765} & & \\\Leftrightarrow & x = \frac{62}{765} & & \\ & V = \left\{ \frac{62}{765} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{+108} & = & \color{red}{315x} +40 \\\Leftrightarrow & -1350x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & -1350x-315x& = & 40-108 \\\Leftrightarrow & \color{red}{-1665} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1665} & & \\\Leftrightarrow & x = \frac{68}{1665} & & \\ & V = \left\{ \frac{68}{1665} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{2})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{25}{2}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x- \frac{125}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{-125} & = & \color{red}{-70x} +12 \\\Leftrightarrow & -200x \color{red}{-125} \color{blue}{+125} \color{blue}{+70x} & = & \color{red}{-70x} +12 \color{blue}{+70x} \color{blue}{+125} \\\Leftrightarrow & -200x+70x& = & 12+125 \\\Leftrightarrow & \color{red}{-130} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-130} & & \\\Leftrightarrow & x = \frac{-137}{130} & & \\ & V = \left\{ \frac{-137}{130} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-210} & = & \color{red}{-385x} +110 \\\Leftrightarrow & -924x \color{red}{-210} \color{blue}{+210} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{+210} \\\Leftrightarrow & -924x+385x& = & 110+210 \\\Leftrightarrow & \color{red}{-539} x& = & 320 \\\Leftrightarrow & x = \frac{320}{-539} & & \\\Leftrightarrow & x = \frac{-320}{539} & & \\ & V = \left\{ \frac{-320}{539} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-126} & = & \color{red}{-539x} +44 \\\Leftrightarrow & -2310x \color{red}{-126} \color{blue}{+126} \color{blue}{+539x} & = & \color{red}{-539x} +44 \color{blue}{+539x} \color{blue}{+126} \\\Leftrightarrow & -2310x+539x& = & 44+126 \\\Leftrightarrow & \color{red}{-1771} x& = & 170 \\\Leftrightarrow & x = \frac{170}{-1771} & & \\\Leftrightarrow & x = \frac{-170}{1771} & & \\ & V = \left\{ \frac{-170}{1771} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{5})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -28x+\frac{14}{5}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-980}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -980x \color{red}{+98} & = & \color{red}{280x} +50 \\\Leftrightarrow & -980x \color{red}{+98} \color{blue}{-98} \color{blue}{-280x} & = & \color{red}{280x} +50 \color{blue}{-280x} \color{blue}{-98} \\\Leftrightarrow & -980x-280x& = & 50-98 \\\Leftrightarrow & \color{red}{-1260} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{-1260} & & \\\Leftrightarrow & x = \frac{4}{105} & & \\ & V = \left\{ \frac{4}{105} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{8})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 25x-\frac{15}{8}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2200}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2200x \color{red}{-165} & = & \color{red}{-792x} +32 \\\Leftrightarrow & 2200x \color{red}{-165} \color{blue}{+165} \color{blue}{+792x} & = & \color{red}{-792x} +32 \color{blue}{+792x} \color{blue}{+165} \\\Leftrightarrow & 2200x+792x& = & 32+165 \\\Leftrightarrow & \color{red}{2992} x& = & 197 \\\Leftrightarrow & x = \frac{197}{2992} & & \\ & V = \left\{ \frac{197}{2992} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-6} & = & \color{red}{-49x} +5 \\\Leftrightarrow & -42x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +5 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & -42x+49x& = & 5+6 \\\Leftrightarrow & \color{red}{7} x& = & 11 \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{-270} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -1512x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & -1512x+315x& = & 56+270 \\\Leftrightarrow & \color{red}{-1197} x& = & 326 \\\Leftrightarrow & x = \frac{326}{-1197} & & \\\Leftrightarrow & x = \frac{-326}{1197} & & \\ & V = \left\{ \frac{-326}{1197} \right\} & \\\end{align}\)