Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{11})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -8x+\frac{10}{11}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{+20} & = & \color{red}{-198x} +55 \\\Leftrightarrow & -176x \color{red}{+20} \color{blue}{-20} \color{blue}{+198x} & = & \color{red}{-198x} +55 \color{blue}{+198x} \color{blue}{-20} \\\Leftrightarrow & -176x+198x& = & 55-20 \\\Leftrightarrow & \color{red}{22} x& = & 35 \\\Leftrightarrow & x = \frac{35}{22} & & \\ & V = \left\{ \frac{35}{22} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{105x} +40 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & 450x-105x& = & 40-72 \\\Leftrightarrow & \color{red}{345} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{345} & & \\ & V = \left\{ \frac{-32}{345} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{5})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 14x+\frac{14}{5}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x+ \frac{28}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{+28} & = & \color{red}{90x} +35 \\\Leftrightarrow & 140x \color{red}{+28} \color{blue}{-28} \color{blue}{-90x} & = & \color{red}{90x} +35 \color{blue}{-90x} \color{blue}{-28} \\\Leftrightarrow & 140x-90x& = & 35-28 \\\Leftrightarrow & \color{red}{50} x& = & 7 \\\Leftrightarrow & x = \frac{7}{50} & & \\ & V = \left\{ \frac{7}{50} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-10} & = & \color{red}{49x} +2 \\\Leftrightarrow & -140x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & -140x-49x& = & 2+10 \\\Leftrightarrow & \color{red}{-189} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-189} & & \\\Leftrightarrow & x = \frac{-4}{63} & & \\ & V = \left\{ \frac{-4}{63} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{11})& = & -4x+\frac{7}{8} \\\Leftrightarrow & -25x+\frac{10}{11}& = & -4x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2200}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{-352}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2200x \color{red}{+80} & = & \color{red}{-352x} +77 \\\Leftrightarrow & -2200x \color{red}{+80} \color{blue}{-80} \color{blue}{+352x} & = & \color{red}{-352x} +77 \color{blue}{+352x} \color{blue}{-80} \\\Leftrightarrow & -2200x+352x& = & 77-80 \\\Leftrightarrow & \color{red}{-1848} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-1848} & & \\\Leftrightarrow & x = \frac{1}{616} & & \\ & V = \left\{ \frac{1}{616} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -4x+\frac{4}{3}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{75x} +24 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{-75x} & = & \color{red}{75x} +24 \color{blue}{-75x} \color{blue}{-20} \\\Leftrightarrow & -60x-75x& = & 24-20 \\\Leftrightarrow & \color{red}{-135} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-135} & & \\\Leftrightarrow & x = \frac{-4}{135} & & \\ & V = \left\{ \frac{-4}{135} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{12})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 28x-\frac{35}{12}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{42}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{-35} & = & \color{red}{-60x} +42 \\\Leftrightarrow & 336x \color{red}{-35} \color{blue}{+35} \color{blue}{+60x} & = & \color{red}{-60x} +42 \color{blue}{+60x} \color{blue}{+35} \\\Leftrightarrow & 336x+60x& = & 42+35 \\\Leftrightarrow & \color{red}{396} x& = & 77 \\\Leftrightarrow & x = \frac{77}{396} & & \\\Leftrightarrow & x = \frac{7}{36} & & \\ & V = \left\{ \frac{7}{36} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{5})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 12x-\frac{16}{5}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{112}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-112} & = & \color{red}{175x} +25 \\\Leftrightarrow & 420x \color{red}{-112} \color{blue}{+112} \color{blue}{-175x} & = & \color{red}{175x} +25 \color{blue}{-175x} \color{blue}{+112} \\\Leftrightarrow & 420x-175x& = & 25+112 \\\Leftrightarrow & \color{red}{245} x& = & 137 \\\Leftrightarrow & x = \frac{137}{245} & & \\ & V = \left\{ \frac{137}{245} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{9})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+40} & = & \color{red}{405x} +54 \\\Leftrightarrow & -360x \color{red}{+40} \color{blue}{-40} \color{blue}{-405x} & = & \color{red}{405x} +54 \color{blue}{-405x} \color{blue}{-40} \\\Leftrightarrow & -360x-405x& = & 54-40 \\\Leftrightarrow & \color{red}{-765} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-765} & & \\\Leftrightarrow & x = \frac{-14}{765} & & \\ & V = \left\{ \frac{-14}{765} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -8x+\frac{16}{7}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+80} & = & \color{red}{315x} +28 \\\Leftrightarrow & -280x \color{red}{+80} \color{blue}{-80} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{-80} \\\Leftrightarrow & -280x-315x& = & 28-80 \\\Leftrightarrow & \color{red}{-595} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-595} & & \\\Leftrightarrow & x = \frac{52}{595} & & \\ & V = \left\{ \frac{52}{595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{2})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{15}{2}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{+165} & = & \color{red}{-154x} +12 \\\Leftrightarrow & 220x \color{red}{+165} \color{blue}{-165} \color{blue}{+154x} & = & \color{red}{-154x} +12 \color{blue}{+154x} \color{blue}{-165} \\\Leftrightarrow & 220x+154x& = & 12-165 \\\Leftrightarrow & \color{red}{374} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{374} & & \\\Leftrightarrow & x = \frac{-9}{22} & & \\ & V = \left\{ \frac{-9}{22} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{8})& = & -7x+\frac{5}{3} \\\Leftrightarrow & -25x+\frac{25}{8}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x+ \frac{75}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{40}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{+75} & = & \color{red}{-168x} +40 \\\Leftrightarrow & -600x \color{red}{+75} \color{blue}{-75} \color{blue}{+168x} & = & \color{red}{-168x} +40 \color{blue}{+168x} \color{blue}{-75} \\\Leftrightarrow & -600x+168x& = & 40-75 \\\Leftrightarrow & \color{red}{-432} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-432} & & \\\Leftrightarrow & x = \frac{35}{432} & & \\ & V = \left\{ \frac{35}{432} \right\} & \\\end{align}\)