Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-18} & = & \color{red}{-168x} +56 \\\Leftrightarrow & -315x \color{red}{-18} \color{blue}{+18} \color{blue}{+168x} & = & \color{red}{-168x} +56 \color{blue}{+168x} \color{blue}{+18} \\\Leftrightarrow & -315x+168x& = & 56+18 \\\Leftrightarrow & \color{red}{-147} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-147} & & \\\Leftrightarrow & x = \frac{-74}{147} & & \\ & V = \left\{ \frac{-74}{147} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -28x-\frac{21}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x- \frac{63}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{-63} & = & \color{red}{75x} +40 \\\Leftrightarrow & -420x \color{red}{-63} \color{blue}{+63} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+63} \\\Leftrightarrow & -420x-75x& = & 40+63 \\\Leftrightarrow & \color{red}{-495} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-495} & & \\\Leftrightarrow & x = \frac{-103}{495} & & \\ & V = \left\{ \frac{-103}{495} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+168} & = & \color{red}{-539x} +110 \\\Leftrightarrow & 924x \color{red}{+168} \color{blue}{-168} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-168} \\\Leftrightarrow & 924x+539x& = & 110-168 \\\Leftrightarrow & \color{red}{1463} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{1463} & & \\ & V = \left\{ \frac{-58}{1463} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 8x-\frac{6}{7}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-6} & = & \color{red}{35x} +3 \\\Leftrightarrow & 56x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & 56x-35x& = & 3+6 \\\Leftrightarrow & \color{red}{21} x& = & 9 \\\Leftrightarrow & x = \frac{9}{21} & & \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{11})& = & -4x+\frac{3}{4} \\\Leftrightarrow & -15x+\frac{10}{11}& = & -4x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+40} & = & \color{red}{-176x} +33 \\\Leftrightarrow & -660x \color{red}{+40} \color{blue}{-40} \color{blue}{+176x} & = & \color{red}{-176x} +33 \color{blue}{+176x} \color{blue}{-40} \\\Leftrightarrow & -660x+176x& = & 33-40 \\\Leftrightarrow & \color{red}{-484} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-484} & & \\\Leftrightarrow & x = \frac{7}{484} & & \\ & V = \left\{ \frac{7}{484} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & -3x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{4}{5}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+8} & = & \color{red}{-30x} +35 \\\Leftrightarrow & -80x \color{red}{+8} \color{blue}{-8} \color{blue}{+30x} & = & \color{red}{-30x} +35 \color{blue}{+30x} \color{blue}{-8} \\\Leftrightarrow & -80x+30x& = & 35-8 \\\Leftrightarrow & \color{red}{-50} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-50} & & \\\Leftrightarrow & x = \frac{-27}{50} & & \\ & V = \left\{ \frac{-27}{50} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{2})& = & 4x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{15}{2}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{+165} & = & \color{red}{88x} +12 \\\Leftrightarrow & -330x \color{red}{+165} \color{blue}{-165} \color{blue}{-88x} & = & \color{red}{88x} +12 \color{blue}{-88x} \color{blue}{-165} \\\Leftrightarrow & -330x-88x& = & 12-165 \\\Leftrightarrow & \color{red}{-418} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{-418} & & \\\Leftrightarrow & x = \frac{153}{418} & & \\ & V = \left\{ \frac{153}{418} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{8})& = & 9x+\frac{7}{11} \\\Leftrightarrow & -35x-\frac{35}{8}& = & 9x+\frac{7}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-3080}{ \color{blue}{88} }x- \frac{385}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{56}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -3080x \color{red}{-385} & = & \color{red}{792x} +56 \\\Leftrightarrow & -3080x \color{red}{-385} \color{blue}{+385} \color{blue}{-792x} & = & \color{red}{792x} +56 \color{blue}{-792x} \color{blue}{+385} \\\Leftrightarrow & -3080x-792x& = & 56+385 \\\Leftrightarrow & \color{red}{-3872} x& = & 441 \\\Leftrightarrow & x = \frac{441}{-3872} & & \\\Leftrightarrow & x = \frac{-441}{3872} & & \\ & V = \left\{ \frac{-441}{3872} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{441x} +56 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{+90} \\\Leftrightarrow & 630x-441x& = & 56+90 \\\Leftrightarrow & \color{red}{189} x& = & 146 \\\Leftrightarrow & x = \frac{146}{189} & & \\ & V = \left\{ \frac{146}{189} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+90} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 660x \color{red}{+90} \color{blue}{-90} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-90} \\\Leftrightarrow & 660x+275x& = & 66-90 \\\Leftrightarrow & \color{red}{935} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{935} & & \\ & V = \left\{ \frac{-24}{935} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{3})& = & -2x+\frac{10}{9} \\\Leftrightarrow & 35x+\frac{7}{3}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{21}{ \color{blue}{9} })& = & (\frac{-18}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+21} & = & \color{red}{-18x} +10 \\\Leftrightarrow & 315x \color{red}{+21} \color{blue}{-21} \color{blue}{+18x} & = & \color{red}{-18x} +10 \color{blue}{+18x} \color{blue}{-21} \\\Leftrightarrow & 315x+18x& = & 10-21 \\\Leftrightarrow & \color{red}{333} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{333} & & \\ & V = \left\{ \frac{-11}{333} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{18}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{90}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{-175x} +42 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+90} \\\Leftrightarrow & -630x+175x& = & 42+90 \\\Leftrightarrow & \color{red}{-455} x& = & 132 \\\Leftrightarrow & x = \frac{132}{-455} & & \\\Leftrightarrow & x = \frac{-132}{455} & & \\ & V = \left\{ \frac{-132}{455} \right\} & \\\end{align}\)