Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 12x-\frac{16}{3}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x- \frac{32}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{-32} & = & \color{red}{30x} +5 \\\Leftrightarrow & 72x \color{red}{-32} \color{blue}{+32} \color{blue}{-30x} & = & \color{red}{30x} +5 \color{blue}{-30x} \color{blue}{+32} \\\Leftrightarrow & 72x-30x& = & 5+32 \\\Leftrightarrow & \color{red}{42} x& = & 37 \\\Leftrightarrow & x = \frac{37}{42} & & \\ & V = \left\{ \frac{37}{42} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{35x} +9 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & 168x-35x& = & 9-30 \\\Leftrightarrow & \color{red}{133} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{133} & & \\\Leftrightarrow & x = \frac{-3}{19} & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 15x-\frac{20}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x- \frac{40}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{-40} & = & \color{red}{154x} +55 \\\Leftrightarrow & 330x \color{red}{-40} \color{blue}{+40} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{+40} \\\Leftrightarrow & 330x-154x& = & 55+40 \\\Leftrightarrow & \color{red}{176} x& = & 95 \\\Leftrightarrow & x = \frac{95}{176} & & \\ & V = \left\{ \frac{95}{176} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{9})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{20}{9}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{-40} & = & \color{red}{-126x} +27 \\\Leftrightarrow & -360x \color{red}{-40} \color{blue}{+40} \color{blue}{+126x} & = & \color{red}{-126x} +27 \color{blue}{+126x} \color{blue}{+40} \\\Leftrightarrow & -360x+126x& = & 27+40 \\\Leftrightarrow & \color{red}{-234} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-234} & & \\\Leftrightarrow & x = \frac{-67}{234} & & \\ & V = \left\{ \frac{-67}{234} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{12})& = & 6x+\frac{8}{3} \\\Leftrightarrow & 35x+\frac{35}{12}& = & 6x+\frac{8}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x+ \frac{35}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{+35} & = & \color{red}{72x} +32 \\\Leftrightarrow & 420x \color{red}{+35} \color{blue}{-35} \color{blue}{-72x} & = & \color{red}{72x} +32 \color{blue}{-72x} \color{blue}{-35} \\\Leftrightarrow & 420x-72x& = & 32-35 \\\Leftrightarrow & \color{red}{348} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{348} & & \\\Leftrightarrow & x = \frac{-1}{116} & & \\ & V = \left\{ \frac{-1}{116} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+100} & = & \color{red}{-75x} +24 \\\Leftrightarrow & -180x \color{red}{+100} \color{blue}{-100} \color{blue}{+75x} & = & \color{red}{-75x} +24 \color{blue}{+75x} \color{blue}{-100} \\\Leftrightarrow & -180x+75x& = & 24-100 \\\Leftrightarrow & \color{red}{-105} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-105} & & \\\Leftrightarrow & x = \frac{76}{105} & & \\ & V = \left\{ \frac{76}{105} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 75x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 75x-35x& = & 6-12 \\\Leftrightarrow & \color{red}{40} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{40} & & \\\Leftrightarrow & x = \frac{-3}{20} & & \\ & V = \left\{ \frac{-3}{20} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{11})& = & 8x+\frac{8}{11} \\\Leftrightarrow & 9x-\frac{12}{11}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{-12} & = & \color{red}{88x} +8 \\\Leftrightarrow & 99x \color{red}{-12} \color{blue}{+12} \color{blue}{-88x} & = & \color{red}{88x} +8 \color{blue}{-88x} \color{blue}{+12} \\\Leftrightarrow & 99x-88x& = & 8+12 \\\Leftrightarrow & \color{red}{11} x& = & 20 \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{-231} & = & \color{red}{-264x} +48 \\\Leftrightarrow & 2464x \color{red}{-231} \color{blue}{+231} \color{blue}{+264x} & = & \color{red}{-264x} +48 \color{blue}{+264x} \color{blue}{+231} \\\Leftrightarrow & 2464x+264x& = & 48+231 \\\Leftrightarrow & \color{red}{2728} x& = & 279 \\\Leftrightarrow & x = \frac{279}{2728} & & \\\Leftrightarrow & x = \frac{9}{88} & & \\ & V = \left\{ \frac{9}{88} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{4})& = & -3x+\frac{7}{6} \\\Leftrightarrow & 20x-\frac{15}{4}& = & -3x+\frac{7}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{14}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{-45} & = & \color{red}{-36x} +14 \\\Leftrightarrow & 240x \color{red}{-45} \color{blue}{+45} \color{blue}{+36x} & = & \color{red}{-36x} +14 \color{blue}{+36x} \color{blue}{+45} \\\Leftrightarrow & 240x+36x& = & 14+45 \\\Leftrightarrow & \color{red}{276} x& = & 59 \\\Leftrightarrow & x = \frac{59}{276} & & \\ & V = \left\{ \frac{59}{276} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{7})& = & -8x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{20}{7}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+20} & = & \color{red}{-56x} +10 \\\Leftrightarrow & -105x \color{red}{+20} \color{blue}{-20} \color{blue}{+56x} & = & \color{red}{-56x} +10 \color{blue}{+56x} \color{blue}{-20} \\\Leftrightarrow & -105x+56x& = & 10-20 \\\Leftrightarrow & \color{red}{-49} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-49} & & \\\Leftrightarrow & x = \frac{10}{49} & & \\ & V = \left\{ \frac{10}{49} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{-175x} +30 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 420x+175x& = & 30-84 \\\Leftrightarrow & \color{red}{595} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{595} & & \\ & V = \left\{ \frac{-54}{595} \right\} & \\\end{align}\)