Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{3})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{-8} & = & \color{red}{21x} +8 \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{+8} \\\Leftrightarrow & 24x-21x& = & 8+8 \\\Leftrightarrow & \color{red}{3} x& = & 16 \\\Leftrightarrow & x = \frac{16}{3} & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{3})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{42x} +9 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{+40} \\\Leftrightarrow & -120x-42x& = & 9+40 \\\Leftrightarrow & \color{red}{-162} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-162} & & \\\Leftrightarrow & x = \frac{-49}{162} & & \\ & V = \left\{ \frac{-49}{162} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 30x-\frac{24}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{-168} & = & \color{red}{-539x} +88 \\\Leftrightarrow & 2310x \color{red}{-168} \color{blue}{+168} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{+168} \\\Leftrightarrow & 2310x+539x& = & 88+168 \\\Leftrightarrow & \color{red}{2849} x& = & 256 \\\Leftrightarrow & x = \frac{256}{2849} & & \\ & V = \left\{ \frac{256}{2849} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{11})& = & 3x+\frac{9}{5} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-50} & = & \color{red}{165x} +99 \\\Leftrightarrow & 550x \color{red}{-50} \color{blue}{+50} \color{blue}{-165x} & = & \color{red}{165x} +99 \color{blue}{-165x} \color{blue}{+50} \\\Leftrightarrow & 550x-165x& = & 99+50 \\\Leftrightarrow & \color{red}{385} x& = & 149 \\\Leftrightarrow & x = \frac{149}{385} & & \\ & V = \left\{ \frac{149}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{2})& = & -4x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{15}{2}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{-75} & = & \color{red}{-40x} +12 \\\Leftrightarrow & 150x \color{red}{-75} \color{blue}{+75} \color{blue}{+40x} & = & \color{red}{-40x} +12 \color{blue}{+40x} \color{blue}{+75} \\\Leftrightarrow & 150x+40x& = & 12+75 \\\Leftrightarrow & \color{red}{190} x& = & 87 \\\Leftrightarrow & x = \frac{87}{190} & & \\ & V = \left\{ \frac{87}{190} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-168} & = & \color{red}{385x} +88 \\\Leftrightarrow & -924x \color{red}{-168} \color{blue}{+168} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+168} \\\Leftrightarrow & -924x-385x& = & 88+168 \\\Leftrightarrow & \color{red}{-1309} x& = & 256 \\\Leftrightarrow & x = \frac{256}{-1309} & & \\\Leftrightarrow & x = \frac{-256}{1309} & & \\ & V = \left\{ \frac{-256}{1309} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 6x+\frac{8}{9}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+88} & = & \color{red}{495x} +36 \\\Leftrightarrow & 594x \color{red}{+88} \color{blue}{-88} \color{blue}{-495x} & = & \color{red}{495x} +36 \color{blue}{-495x} \color{blue}{-88} \\\Leftrightarrow & 594x-495x& = & 36-88 \\\Leftrightarrow & \color{red}{99} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{99} & & \\ & V = \left\{ \frac{-52}{99} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 28x-\frac{21}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-63} & = & \color{red}{-297x} +44 \\\Leftrightarrow & 924x \color{red}{-63} \color{blue}{+63} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+63} \\\Leftrightarrow & 924x+297x& = & 44+63 \\\Leftrightarrow & \color{red}{1221} x& = & 107 \\\Leftrightarrow & x = \frac{107}{1221} & & \\ & V = \left\{ \frac{107}{1221} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-90} \\\Leftrightarrow & -990x+693x& = & 110-90 \\\Leftrightarrow & \color{red}{-297} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-297} & & \\\Leftrightarrow & x = \frac{-20}{297} & & \\ & V = \left\{ \frac{-20}{297} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+8} & = & \color{red}{63x} +6 \\\Leftrightarrow & -90x \color{red}{+8} \color{blue}{-8} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{-8} \\\Leftrightarrow & -90x-63x& = & 6-8 \\\Leftrightarrow & \color{red}{-153} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-153} & & \\\Leftrightarrow & x = \frac{2}{153} & & \\ & V = \left\{ \frac{2}{153} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{5})& = & -8x+\frac{10}{7} \\\Leftrightarrow & 15x-\frac{6}{5}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-42} & = & \color{red}{-280x} +50 \\\Leftrightarrow & 525x \color{red}{-42} \color{blue}{+42} \color{blue}{+280x} & = & \color{red}{-280x} +50 \color{blue}{+280x} \color{blue}{+42} \\\Leftrightarrow & 525x+280x& = & 50+42 \\\Leftrightarrow & \color{red}{805} x& = & 92 \\\Leftrightarrow & x = \frac{92}{805} & & \\\Leftrightarrow & x = \frac{4}{35} & & \\ & V = \left\{ \frac{4}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+24} & = & \color{red}{-50x} +3 \\\Leftrightarrow & 60x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & 60x+50x& = & 3-24 \\\Leftrightarrow & \color{red}{110} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{110} & & \\ & V = \left\{ \frac{-21}{110} \right\} & \\\end{align}\)