Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{18}{11}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-126} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 924x \color{red}{-126} \color{blue}{+126} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+126} \\\Leftrightarrow & 924x+385x& = & 66+126 \\\Leftrightarrow & \color{red}{1309} x& = & 192 \\\Leftrightarrow & x = \frac{192}{1309} & & \\ & V = \left\{ \frac{192}{1309} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{1}{2})& = & 7x+\frac{7}{6} \\\Leftrightarrow & 20x-\frac{5}{2}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{15}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-15} & = & \color{red}{42x} +7 \\\Leftrightarrow & 120x \color{red}{-15} \color{blue}{+15} \color{blue}{-42x} & = & \color{red}{42x} +7 \color{blue}{-42x} \color{blue}{+15} \\\Leftrightarrow & 120x-42x& = & 7+15 \\\Leftrightarrow & \color{red}{78} x& = & 22 \\\Leftrightarrow & x = \frac{22}{78} & & \\\Leftrightarrow & x = \frac{11}{39} & & \\ & V = \left\{ \frac{11}{39} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{9}{5} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+12} & = & \color{red}{-25x} +9 \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +9 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 30x+25x& = & 9-12 \\\Leftrightarrow & \color{red}{55} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{55} & & \\ & V = \left\{ \frac{-3}{55} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-36} & = & \color{red}{75x} +35 \\\Leftrightarrow & 90x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +35 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 90x-75x& = & 35+36 \\\Leftrightarrow & \color{red}{15} x& = & 71 \\\Leftrightarrow & x = \frac{71}{15} & & \\ & V = \left\{ \frac{71}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{5})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 8x+\frac{16}{5}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x+ \frac{16}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{+16} & = & \color{red}{15x} +4 \\\Leftrightarrow & 40x \color{red}{+16} \color{blue}{-16} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{-16} \\\Leftrightarrow & 40x-15x& = & 4-16 \\\Leftrightarrow & \color{red}{25} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{25} & & \\ & V = \left\{ \frac{-12}{25} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -21x+\frac{28}{3}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{+28} & = & \color{red}{-24x} +10 \\\Leftrightarrow & -63x \color{red}{+28} \color{blue}{-28} \color{blue}{+24x} & = & \color{red}{-24x} +10 \color{blue}{+24x} \color{blue}{-28} \\\Leftrightarrow & -63x+24x& = & 10-28 \\\Leftrightarrow & \color{red}{-39} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-39} & & \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 24x+\frac{12}{11}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{+24} & = & \color{red}{110x} +33 \\\Leftrightarrow & 528x \color{red}{+24} \color{blue}{-24} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{-24} \\\Leftrightarrow & 528x-110x& = & 33-24 \\\Leftrightarrow & \color{red}{418} x& = & 9 \\\Leftrightarrow & x = \frac{9}{418} & & \\ & V = \left\{ \frac{9}{418} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{7})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -20x+\frac{20}{7}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+20} & = & \color{red}{-63x} +9 \\\Leftrightarrow & -140x \color{red}{+20} \color{blue}{-20} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{-20} \\\Leftrightarrow & -140x+63x& = & 9-20 \\\Leftrightarrow & \color{red}{-77} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-77} & & \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 660x+275x& = & 30-132 \\\Leftrightarrow & \color{red}{935} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{935} & & \\\Leftrightarrow & x = \frac{-6}{55} & & \\ & V = \left\{ \frac{-6}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{11})& = & 5x+\frac{9}{11} \\\Leftrightarrow & -12x+\frac{8}{11}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+8} & = & \color{red}{55x} +9 \\\Leftrightarrow & -132x \color{red}{+8} \color{blue}{-8} \color{blue}{-55x} & = & \color{red}{55x} +9 \color{blue}{-55x} \color{blue}{-8} \\\Leftrightarrow & -132x-55x& = & 9-8 \\\Leftrightarrow & \color{red}{-187} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-187} & & \\\Leftrightarrow & x = \frac{-1}{187} & & \\ & V = \left\{ \frac{-1}{187} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x-\frac{15}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{15}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-15} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -84x \color{red}{-15} \color{blue}{+15} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{+15} \\\Leftrightarrow & -84x+35x& = & 2+15 \\\Leftrightarrow & \color{red}{-49} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-49} & & \\\Leftrightarrow & x = \frac{-17}{49} & & \\ & V = \left\{ \frac{-17}{49} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{7})& = & 8x+\frac{10}{7} \\\Leftrightarrow & 25x+\frac{15}{7}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{+15} & = & \color{red}{56x} +10 \\\Leftrightarrow & 175x \color{red}{+15} \color{blue}{-15} \color{blue}{-56x} & = & \color{red}{56x} +10 \color{blue}{-56x} \color{blue}{-15} \\\Leftrightarrow & 175x-56x& = & 10-15 \\\Leftrightarrow & \color{red}{119} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{119} & & \\ & V = \left\{ \frac{-5}{119} \right\} & \\\end{align}\)