Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+1)& = & -2x+\frac{8}{3} \\\Leftrightarrow & 21x-7& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x- \frac{21}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{-21} & = & \color{red}{-6x} +8 \\\Leftrightarrow & 63x \color{red}{-21} \color{blue}{+21} \color{blue}{+6x} & = & \color{red}{-6x} +8 \color{blue}{+6x} \color{blue}{+21} \\\Leftrightarrow & 63x+6x& = & 8+21 \\\Leftrightarrow & \color{red}{69} x& = & 29 \\\Leftrightarrow & x = \frac{29}{69} & & \\ & V = \left\{ \frac{29}{69} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+54} & = & \color{red}{315x} +35 \\\Leftrightarrow & 378x \color{red}{+54} \color{blue}{-54} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{-54} \\\Leftrightarrow & 378x-315x& = & 35-54 \\\Leftrightarrow & \color{red}{63} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{63} & & \\ & V = \left\{ \frac{-19}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-84} & = & \color{red}{245x} +30 \\\Leftrightarrow & 560x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +30 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & 560x-245x& = & 30+84 \\\Leftrightarrow & \color{red}{315} x& = & 114 \\\Leftrightarrow & x = \frac{114}{315} & & \\\Leftrightarrow & x = \frac{38}{105} & & \\ & V = \left\{ \frac{38}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+150} & = & \color{red}{280x} +42 \\\Leftrightarrow & -630x \color{red}{+150} \color{blue}{-150} \color{blue}{-280x} & = & \color{red}{280x} +42 \color{blue}{-280x} \color{blue}{-150} \\\Leftrightarrow & -630x-280x& = & 42-150 \\\Leftrightarrow & \color{red}{-910} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{-910} & & \\\Leftrightarrow & x = \frac{54}{455} & & \\ & V = \left\{ \frac{54}{455} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{3})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{-14} & = & \color{red}{24x} +10 \\\Leftrightarrow & -84x \color{red}{-14} \color{blue}{+14} \color{blue}{-24x} & = & \color{red}{24x} +10 \color{blue}{-24x} \color{blue}{+14} \\\Leftrightarrow & -84x-24x& = & 10+14 \\\Leftrightarrow & \color{red}{-108} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-108} & & \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{5})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 9x+\frac{6}{5}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{+24} & = & \color{red}{140x} +15 \\\Leftrightarrow & 180x \color{red}{+24} \color{blue}{-24} \color{blue}{-140x} & = & \color{red}{140x} +15 \color{blue}{-140x} \color{blue}{-24} \\\Leftrightarrow & 180x-140x& = & 15-24 \\\Leftrightarrow & \color{red}{40} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{40} & & \\ & V = \left\{ \frac{-9}{40} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{8})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -20x-\frac{15}{8}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{-45} & = & \color{red}{-72x} +20 \\\Leftrightarrow & -480x \color{red}{-45} \color{blue}{+45} \color{blue}{+72x} & = & \color{red}{-72x} +20 \color{blue}{+72x} \color{blue}{+45} \\\Leftrightarrow & -480x+72x& = & 20+45 \\\Leftrightarrow & \color{red}{-408} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-408} & & \\\Leftrightarrow & x = \frac{-65}{408} & & \\ & V = \left\{ \frac{-65}{408} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{10})& = & 8x+\frac{5}{3} \\\Leftrightarrow & -21x+\frac{21}{10}& = & 8x+\frac{5}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x+ \frac{63}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{50}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{+63} & = & \color{red}{240x} +50 \\\Leftrightarrow & -630x \color{red}{+63} \color{blue}{-63} \color{blue}{-240x} & = & \color{red}{240x} +50 \color{blue}{-240x} \color{blue}{-63} \\\Leftrightarrow & -630x-240x& = & 50-63 \\\Leftrightarrow & \color{red}{-870} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-870} & & \\\Leftrightarrow & x = \frac{13}{870} & & \\ & V = \left\{ \frac{13}{870} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{2})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{15}{2}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{135}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+135} & = & \color{red}{-126x} +16 \\\Leftrightarrow & 360x \color{red}{+135} \color{blue}{-135} \color{blue}{+126x} & = & \color{red}{-126x} +16 \color{blue}{+126x} \color{blue}{-135} \\\Leftrightarrow & 360x+126x& = & 16-135 \\\Leftrightarrow & \color{red}{486} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{486} & & \\ & V = \left\{ \frac{-119}{486} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 28x+\frac{21}{8}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1120}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1120x \color{red}{+105} & = & \color{red}{200x} +36 \\\Leftrightarrow & 1120x \color{red}{+105} \color{blue}{-105} \color{blue}{-200x} & = & \color{red}{200x} +36 \color{blue}{-200x} \color{blue}{-105} \\\Leftrightarrow & 1120x-200x& = & 36-105 \\\Leftrightarrow & \color{red}{920} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{920} & & \\\Leftrightarrow & x = \frac{-3}{40} & & \\ & V = \left\{ \frac{-3}{40} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 15x-\frac{15}{11}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{-154x} +55 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{+154x} & = & \color{red}{-154x} +55 \color{blue}{+154x} \color{blue}{+30} \\\Leftrightarrow & 330x+154x& = & 55+30 \\\Leftrightarrow & \color{red}{484} x& = & 85 \\\Leftrightarrow & x = \frac{85}{484} & & \\ & V = \left\{ \frac{85}{484} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{11})& = & -6x+\frac{6}{7} \\\Leftrightarrow & -25x-\frac{10}{11}& = & -6x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{-70} & = & \color{red}{-462x} +66 \\\Leftrightarrow & -1925x \color{red}{-70} \color{blue}{+70} \color{blue}{+462x} & = & \color{red}{-462x} +66 \color{blue}{+462x} \color{blue}{+70} \\\Leftrightarrow & -1925x+462x& = & 66+70 \\\Leftrightarrow & \color{red}{-1463} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-1463} & & \\\Leftrightarrow & x = \frac{-136}{1463} & & \\ & V = \left\{ \frac{-136}{1463} \right\} & \\\end{align}\)