Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{+28} & = & \color{red}{315x} +40 \\\Leftrightarrow & -140x \color{red}{+28} \color{blue}{-28} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-28} \\\Leftrightarrow & -140x-315x& = & 40-28 \\\Leftrightarrow & \color{red}{-455} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-455} & & \\\Leftrightarrow & x = \frac{-12}{455} & & \\ & V = \left\{ \frac{-12}{455} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 12x-\frac{18}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{+18} \\\Leftrightarrow & 60x+25x& = & 4+18 \\\Leftrightarrow & \color{red}{85} x& = & 22 \\\Leftrightarrow & x = \frac{22}{85} & & \\ & V = \left\{ \frac{22}{85} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{11})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{4}{11}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{12}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-12} & = & \color{red}{-297x} +22 \\\Leftrightarrow & -264x \color{red}{-12} \color{blue}{+12} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{+12} \\\Leftrightarrow & -264x+297x& = & 22+12 \\\Leftrightarrow & \color{red}{33} x& = & 34 \\\Leftrightarrow & x = \frac{34}{33} & & \\ & V = \left\{ \frac{34}{33} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{9})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -4x-\frac{10}{9}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{50}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-50} & = & \color{red}{405x} +54 \\\Leftrightarrow & -180x \color{red}{-50} \color{blue}{+50} \color{blue}{-405x} & = & \color{red}{405x} +54 \color{blue}{-405x} \color{blue}{+50} \\\Leftrightarrow & -180x-405x& = & 54+50 \\\Leftrightarrow & \color{red}{-585} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-585} & & \\\Leftrightarrow & x = \frac{-8}{45} & & \\ & V = \left\{ \frac{-8}{45} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{8}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-8} & = & \color{red}{49x} +10 \\\Leftrightarrow & -42x \color{red}{-8} \color{blue}{+8} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{+8} \\\Leftrightarrow & -42x-49x& = & 10+8 \\\Leftrightarrow & \color{red}{-91} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-91} & & \\\Leftrightarrow & x = \frac{-18}{91} & & \\ & V = \left\{ \frac{-18}{91} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 30x-\frac{24}{5}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{600}{ \color{blue}{20} }x- \frac{96}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 600x \color{red}{-96} & = & \color{red}{-140x} +15 \\\Leftrightarrow & 600x \color{red}{-96} \color{blue}{+96} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{+96} \\\Leftrightarrow & 600x+140x& = & 15+96 \\\Leftrightarrow & \color{red}{740} x& = & 111 \\\Leftrightarrow & x = \frac{111}{740} & & \\\Leftrightarrow & x = \frac{3}{20} & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 6x-\frac{9}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x- \frac{9}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{-9} & = & \color{red}{49x} +2 \\\Leftrightarrow & 42x \color{red}{-9} \color{blue}{+9} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{+9} \\\Leftrightarrow & 42x-49x& = & 2+9 \\\Leftrightarrow & \color{red}{-7} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-7} & & \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{15}{4}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-60}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{+75} & = & \color{red}{-60x} +24 \\\Leftrightarrow & -400x \color{red}{+75} \color{blue}{-75} \color{blue}{+60x} & = & \color{red}{-60x} +24 \color{blue}{+60x} \color{blue}{-75} \\\Leftrightarrow & -400x+60x& = & 24-75 \\\Leftrightarrow & \color{red}{-340} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-340} & & \\\Leftrightarrow & x = \frac{3}{20} & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{8})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -9x+\frac{15}{8}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{40}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{+165} & = & \color{red}{440x} +40 \\\Leftrightarrow & -792x \color{red}{+165} \color{blue}{-165} \color{blue}{-440x} & = & \color{red}{440x} +40 \color{blue}{-440x} \color{blue}{-165} \\\Leftrightarrow & -792x-440x& = & 40-165 \\\Leftrightarrow & \color{red}{-1232} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-1232} & & \\\Leftrightarrow & x = \frac{125}{1232} & & \\ & V = \left\{ \frac{125}{1232} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{11})& = & -3x+\frac{5}{9} \\\Leftrightarrow & -14x+\frac{35}{11}& = & -3x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{315}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+315} & = & \color{red}{-297x} +55 \\\Leftrightarrow & -1386x \color{red}{+315} \color{blue}{-315} \color{blue}{+297x} & = & \color{red}{-297x} +55 \color{blue}{+297x} \color{blue}{-315} \\\Leftrightarrow & -1386x+297x& = & 55-315 \\\Leftrightarrow & \color{red}{-1089} x& = & -260 \\\Leftrightarrow & x = \frac{-260}{-1089} & & \\\Leftrightarrow & x = \frac{260}{1089} & & \\ & V = \left\{ \frac{260}{1089} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{3})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{8}{3}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+56} & = & \color{red}{105x} +30 \\\Leftrightarrow & -252x \color{red}{+56} \color{blue}{-56} \color{blue}{-105x} & = & \color{red}{105x} +30 \color{blue}{-105x} \color{blue}{-56} \\\Leftrightarrow & -252x-105x& = & 30-56 \\\Leftrightarrow & \color{red}{-357} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-357} & & \\\Leftrightarrow & x = \frac{26}{357} & & \\ & V = \left\{ \frac{26}{357} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-784}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -784x \color{red}{+147} & = & \color{red}{280x} +48 \\\Leftrightarrow & -784x \color{red}{+147} \color{blue}{-147} \color{blue}{-280x} & = & \color{red}{280x} +48 \color{blue}{-280x} \color{blue}{-147} \\\Leftrightarrow & -784x-280x& = & 48-147 \\\Leftrightarrow & \color{red}{-1064} x& = & -99 \\\Leftrightarrow & x = \frac{-99}{-1064} & & \\\Leftrightarrow & x = \frac{99}{1064} & & \\ & V = \left\{ \frac{99}{1064} \right\} & \\\end{align}\)