Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-30} & = & \color{red}{175x} +56 \\\Leftrightarrow & 210x \color{red}{-30} \color{blue}{+30} \color{blue}{-175x} & = & \color{red}{175x} +56 \color{blue}{-175x} \color{blue}{+30} \\\Leftrightarrow & 210x-175x& = & 56+30 \\\Leftrightarrow & \color{red}{35} x& = & 86 \\\Leftrightarrow & x = \frac{86}{35} & & \\ & V = \left\{ \frac{86}{35} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-330} & = & \color{red}{-385x} +28 \\\Leftrightarrow & -1848x \color{red}{-330} \color{blue}{+330} \color{blue}{+385x} & = & \color{red}{-385x} +28 \color{blue}{+385x} \color{blue}{+330} \\\Leftrightarrow & -1848x+385x& = & 28+330 \\\Leftrightarrow & \color{red}{-1463} x& = & 358 \\\Leftrightarrow & x = \frac{358}{-1463} & & \\\Leftrightarrow & x = \frac{-358}{1463} & & \\ & V = \left\{ \frac{-358}{1463} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{11})& = & 2x+\frac{3}{10} \\\Leftrightarrow & 9x-\frac{9}{11}& = & 2x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{990}{ \color{blue}{110} }x- \frac{90}{ \color{blue}{110} })& = & (\frac{220}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 990x \color{red}{-90} & = & \color{red}{220x} +33 \\\Leftrightarrow & 990x \color{red}{-90} \color{blue}{+90} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{+90} \\\Leftrightarrow & 990x-220x& = & 33+90 \\\Leftrightarrow & \color{red}{770} x& = & 123 \\\Leftrightarrow & x = \frac{123}{770} & & \\ & V = \left\{ \frac{123}{770} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{7})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -8x+\frac{20}{7}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-224}{ \color{blue}{28} }x+ \frac{80}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -224x \color{red}{+80} & = & \color{red}{252x} +63 \\\Leftrightarrow & -224x \color{red}{+80} \color{blue}{-80} \color{blue}{-252x} & = & \color{red}{252x} +63 \color{blue}{-252x} \color{blue}{-80} \\\Leftrightarrow & -224x-252x& = & 63-80 \\\Leftrightarrow & \color{red}{-476} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-476} & & \\\Leftrightarrow & x = \frac{1}{28} & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{11})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 25x-\frac{15}{11}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{275}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 275x \color{red}{-15} & = & \color{red}{77x} +2 \\\Leftrightarrow & 275x \color{red}{-15} \color{blue}{+15} \color{blue}{-77x} & = & \color{red}{77x} +2 \color{blue}{-77x} \color{blue}{+15} \\\Leftrightarrow & 275x-77x& = & 2+15 \\\Leftrightarrow & \color{red}{198} x& = & 17 \\\Leftrightarrow & x = \frac{17}{198} & & \\ & V = \left\{ \frac{17}{198} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & 4x+\frac{9}{10} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+24} & = & \color{red}{40x} +9 \\\Leftrightarrow & -150x \color{red}{+24} \color{blue}{-24} \color{blue}{-40x} & = & \color{red}{40x} +9 \color{blue}{-40x} \color{blue}{-24} \\\Leftrightarrow & -150x-40x& = & 9-24 \\\Leftrightarrow & \color{red}{-190} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-190} & & \\\Leftrightarrow & x = \frac{3}{38} & & \\ & V = \left\{ \frac{3}{38} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{2})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 14x+\frac{35}{2}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{28}{ \color{blue}{2} }x+ \frac{35}{ \color{blue}{2} })& = & (\frac{-6}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 28x \color{red}{+35} & = & \color{red}{-6x} +5 \\\Leftrightarrow & 28x \color{red}{+35} \color{blue}{-35} \color{blue}{+6x} & = & \color{red}{-6x} +5 \color{blue}{+6x} \color{blue}{-35} \\\Leftrightarrow & 28x+6x& = & 5-35 \\\Leftrightarrow & \color{red}{34} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{34} & & \\\Leftrightarrow & x = \frac{-15}{17} & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{8})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{15}{8}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-165} & = & \color{red}{-440x} +48 \\\Leftrightarrow & -1056x \color{red}{-165} \color{blue}{+165} \color{blue}{+440x} & = & \color{red}{-440x} +48 \color{blue}{+440x} \color{blue}{+165} \\\Leftrightarrow & -1056x+440x& = & 48+165 \\\Leftrightarrow & \color{red}{-616} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-616} & & \\\Leftrightarrow & x = \frac{-213}{616} & & \\ & V = \left\{ \frac{-213}{616} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{2})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{15}{2}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+45} & = & \color{red}{-42x} +8 \\\Leftrightarrow & -120x \color{red}{+45} \color{blue}{-45} \color{blue}{+42x} & = & \color{red}{-42x} +8 \color{blue}{+42x} \color{blue}{-45} \\\Leftrightarrow & -120x+42x& = & 8-45 \\\Leftrightarrow & \color{red}{-78} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-78} & & \\\Leftrightarrow & x = \frac{37}{78} & & \\ & V = \left\{ \frac{37}{78} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{5})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{9}{5}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{20}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-9} & = & \color{red}{20x} +6 \\\Leftrightarrow & -75x \color{red}{-9} \color{blue}{+9} \color{blue}{-20x} & = & \color{red}{20x} +6 \color{blue}{-20x} \color{blue}{+9} \\\Leftrightarrow & -75x-20x& = & 6+9 \\\Leftrightarrow & \color{red}{-95} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-95} & & \\\Leftrightarrow & x = \frac{-3}{19} & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & 8x+\frac{4}{11} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 8x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{352}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{-165} & = & \color{red}{352x} +16 \\\Leftrightarrow & -660x \color{red}{-165} \color{blue}{+165} \color{blue}{-352x} & = & \color{red}{352x} +16 \color{blue}{-352x} \color{blue}{+165} \\\Leftrightarrow & -660x-352x& = & 16+165 \\\Leftrightarrow & \color{red}{-1012} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-1012} & & \\\Leftrightarrow & x = \frac{-181}{1012} & & \\ & V = \left\{ \frac{-181}{1012} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +30 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 30-132 \\\Leftrightarrow & \color{red}{-935} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-935} & & \\\Leftrightarrow & x = \frac{6}{55} & & \\ & V = \left\{ \frac{6}{55} \right\} & \\\end{align}\)