Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{8})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 9x-\frac{15}{8}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{792}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 792x \color{red}{-165} & = & \color{red}{440x} +48 \\\Leftrightarrow & 792x \color{red}{-165} \color{blue}{+165} \color{blue}{-440x} & = & \color{red}{440x} +48 \color{blue}{-440x} \color{blue}{+165} \\\Leftrightarrow & 792x-440x& = & 48+165 \\\Leftrightarrow & \color{red}{352} x& = & 213 \\\Leftrightarrow & x = \frac{213}{352} & & \\ & V = \left\{ \frac{213}{352} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{7})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{8}{7}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{88}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-88} & = & \color{red}{-385x} +35 \\\Leftrightarrow & -924x \color{red}{-88} \color{blue}{+88} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{+88} \\\Leftrightarrow & -924x+385x& = & 35+88 \\\Leftrightarrow & \color{red}{-539} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-539} & & \\\Leftrightarrow & x = \frac{-123}{539} & & \\ & V = \left\{ \frac{-123}{539} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{9})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -16x-\frac{20}{9}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{-140} & = & \color{red}{-441x} +90 \\\Leftrightarrow & -1008x \color{red}{-140} \color{blue}{+140} \color{blue}{+441x} & = & \color{red}{-441x} +90 \color{blue}{+441x} \color{blue}{+140} \\\Leftrightarrow & -1008x+441x& = & 90+140 \\\Leftrightarrow & \color{red}{-567} x& = & 230 \\\Leftrightarrow & x = \frac{230}{-567} & & \\\Leftrightarrow & x = \frac{-230}{567} & & \\ & V = \left\{ \frac{-230}{567} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{7}{3} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-36} & = & \color{red}{105x} +35 \\\Leftrightarrow & -240x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +35 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -240x-105x& = & 35+36 \\\Leftrightarrow & \color{red}{-345} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-345} & & \\\Leftrightarrow & x = \frac{-71}{345} & & \\ & V = \left\{ \frac{-71}{345} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{7})& = & -4x+\frac{8}{11} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -4x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-110} & = & \color{red}{-308x} +56 \\\Leftrightarrow & -1155x \color{red}{-110} \color{blue}{+110} \color{blue}{+308x} & = & \color{red}{-308x} +56 \color{blue}{+308x} \color{blue}{+110} \\\Leftrightarrow & -1155x+308x& = & 56+110 \\\Leftrightarrow & \color{red}{-847} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-847} & & \\\Leftrightarrow & x = \frac{-166}{847} & & \\ & V = \left\{ \frac{-166}{847} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{4})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 15x+\frac{25}{4}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x+ \frac{50}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{+50} & = & \color{red}{-56x} +7 \\\Leftrightarrow & 120x \color{red}{+50} \color{blue}{-50} \color{blue}{+56x} & = & \color{red}{-56x} +7 \color{blue}{+56x} \color{blue}{-50} \\\Leftrightarrow & 120x+56x& = & 7-50 \\\Leftrightarrow & \color{red}{176} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{176} & & \\ & V = \left\{ \frac{-43}{176} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-264} & = & \color{red}{275x} +10 \\\Leftrightarrow & -990x \color{red}{-264} \color{blue}{+264} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+264} \\\Leftrightarrow & -990x-275x& = & 10+264 \\\Leftrightarrow & \color{red}{-1265} x& = & 274 \\\Leftrightarrow & x = \frac{274}{-1265} & & \\\Leftrightarrow & x = \frac{-274}{1265} & & \\ & V = \left\{ \frac{-274}{1265} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{7})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 15x-\frac{15}{7}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-165} & = & \color{red}{-539x} +56 \\\Leftrightarrow & 1155x \color{red}{-165} \color{blue}{+165} \color{blue}{+539x} & = & \color{red}{-539x} +56 \color{blue}{+539x} \color{blue}{+165} \\\Leftrightarrow & 1155x+539x& = & 56+165 \\\Leftrightarrow & \color{red}{1694} x& = & 221 \\\Leftrightarrow & x = \frac{221}{1694} & & \\ & V = \left\{ \frac{221}{1694} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & 2x+\frac{8}{5} \\\Leftrightarrow & 9x+\frac{12}{5}& = & 2x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{10}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{+12} & = & \color{red}{10x} +8 \\\Leftrightarrow & 45x \color{red}{+12} \color{blue}{-12} \color{blue}{-10x} & = & \color{red}{10x} +8 \color{blue}{-10x} \color{blue}{-12} \\\Leftrightarrow & 45x-10x& = & 8-12 \\\Leftrightarrow & \color{red}{35} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{35} & & \\ & V = \left\{ \frac{-4}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 28x+\frac{28}{9}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1764}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1764x \color{red}{+196} & = & \color{red}{-567x} +90 \\\Leftrightarrow & 1764x \color{red}{+196} \color{blue}{-196} \color{blue}{+567x} & = & \color{red}{-567x} +90 \color{blue}{+567x} \color{blue}{-196} \\\Leftrightarrow & 1764x+567x& = & 90-196 \\\Leftrightarrow & \color{red}{2331} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{2331} & & \\ & V = \left\{ \frac{-106}{2331} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -30x+\frac{18}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+198} & = & \color{red}{-385x} +10 \\\Leftrightarrow & -1650x \color{red}{+198} \color{blue}{-198} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{-198} \\\Leftrightarrow & -1650x+385x& = & 10-198 \\\Leftrightarrow & \color{red}{-1265} x& = & -188 \\\Leftrightarrow & x = \frac{-188}{-1265} & & \\\Leftrightarrow & x = \frac{188}{1265} & & \\ & V = \left\{ \frac{188}{1265} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-84} & = & \color{red}{175x} +50 \\\Leftrightarrow & 210x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 210x-175x& = & 50+84 \\\Leftrightarrow & \color{red}{35} x& = & 134 \\\Leftrightarrow & x = \frac{134}{35} & & \\ & V = \left\{ \frac{134}{35} \right\} & \\\end{align}\)