Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & 4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 4x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{-24} & = & \color{red}{40x} +15 \\\Leftrightarrow & -150x \color{red}{-24} \color{blue}{+24} \color{blue}{-40x} & = & \color{red}{40x} +15 \color{blue}{-40x} \color{blue}{+24} \\\Leftrightarrow & -150x-40x& = & 15+24 \\\Leftrightarrow & \color{red}{-190} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-190} & & \\\Leftrightarrow & x = \frac{-39}{190} & & \\ & V = \left\{ \frac{-39}{190} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{560}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 560x \color{red}{-100} & = & \color{red}{490x} +63 \\\Leftrightarrow & 560x \color{red}{-100} \color{blue}{+100} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+100} \\\Leftrightarrow & 560x-490x& = & 63+100 \\\Leftrightarrow & \color{red}{70} x& = & 163 \\\Leftrightarrow & x = \frac{163}{70} & & \\ & V = \left\{ \frac{163}{70} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & -4x+\frac{9}{7} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{-105} & = & \color{red}{-112x} +36 \\\Leftrightarrow & -420x \color{red}{-105} \color{blue}{+105} \color{blue}{+112x} & = & \color{red}{-112x} +36 \color{blue}{+112x} \color{blue}{+105} \\\Leftrightarrow & -420x+112x& = & 36+105 \\\Leftrightarrow & \color{red}{-308} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-308} & & \\\Leftrightarrow & x = \frac{-141}{308} & & \\ & V = \left\{ \frac{-141}{308} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+90} & = & \color{red}{-315x} +28 \\\Leftrightarrow & 252x \color{red}{+90} \color{blue}{-90} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{-90} \\\Leftrightarrow & 252x+315x& = & 28-90 \\\Leftrightarrow & \color{red}{567} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{567} & & \\ & V = \left\{ \frac{-62}{567} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{7}{3} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-36} & = & \color{red}{105x} +35 \\\Leftrightarrow & -240x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +35 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -240x-105x& = & 35+36 \\\Leftrightarrow & \color{red}{-345} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-345} & & \\\Leftrightarrow & x = \frac{-71}{345} & & \\ & V = \left\{ \frac{-71}{345} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{7})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{10}{7}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+20} & = & \color{red}{98x} +35 \\\Leftrightarrow & 112x \color{red}{+20} \color{blue}{-20} \color{blue}{-98x} & = & \color{red}{98x} +35 \color{blue}{-98x} \color{blue}{-20} \\\Leftrightarrow & 112x-98x& = & 35-20 \\\Leftrightarrow & \color{red}{14} x& = & 15 \\\Leftrightarrow & x = \frac{15}{14} & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{9})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{-80} & = & \color{red}{-630x} +27 \\\Leftrightarrow & 540x \color{red}{-80} \color{blue}{+80} \color{blue}{+630x} & = & \color{red}{-630x} +27 \color{blue}{+630x} \color{blue}{+80} \\\Leftrightarrow & 540x+630x& = & 27+80 \\\Leftrightarrow & \color{red}{1170} x& = & 107 \\\Leftrightarrow & x = \frac{107}{1170} & & \\ & V = \left\{ \frac{107}{1170} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{11})& = & 7x+\frac{3}{5} \\\Leftrightarrow & 30x+\frac{24}{11}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+120} & = & \color{red}{385x} +33 \\\Leftrightarrow & 1650x \color{red}{+120} \color{blue}{-120} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{-120} \\\Leftrightarrow & 1650x-385x& = & 33-120 \\\Leftrightarrow & \color{red}{1265} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{1265} & & \\ & V = \left\{ \frac{-87}{1265} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{2})& = & 4x+\frac{5}{2} \\\Leftrightarrow & -15x+\frac{15}{2}& = & 4x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-30}{ \color{blue}{2} }x+ \frac{15}{ \color{blue}{2} })& = & (\frac{8}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -30x \color{red}{+15} & = & \color{red}{8x} +5 \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{-8x} & = & \color{red}{8x} +5 \color{blue}{-8x} \color{blue}{-15} \\\Leftrightarrow & -30x-8x& = & 5-15 \\\Leftrightarrow & \color{red}{-38} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-38} & & \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -4x-\frac{10}{7}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-224}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -224x \color{red}{-80} & = & \color{red}{280x} +35 \\\Leftrightarrow & -224x \color{red}{-80} \color{blue}{+80} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{+80} \\\Leftrightarrow & -224x-280x& = & 35+80 \\\Leftrightarrow & \color{red}{-504} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-504} & & \\\Leftrightarrow & x = \frac{-115}{504} & & \\ & V = \left\{ \frac{-115}{504} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -8x+\frac{6}{5}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+6} & = & \color{red}{-45x} +8 \\\Leftrightarrow & -40x \color{red}{+6} \color{blue}{-6} \color{blue}{+45x} & = & \color{red}{-45x} +8 \color{blue}{+45x} \color{blue}{-6} \\\Leftrightarrow & -40x+45x& = & 8-6 \\\Leftrightarrow & \color{red}{5} x& = & 2 \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{9})& = & -9x+\frac{3}{7} \\\Leftrightarrow & 10x-\frac{20}{9}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-140} & = & \color{red}{-567x} +27 \\\Leftrightarrow & 630x \color{red}{-140} \color{blue}{+140} \color{blue}{+567x} & = & \color{red}{-567x} +27 \color{blue}{+567x} \color{blue}{+140} \\\Leftrightarrow & 630x+567x& = & 27+140 \\\Leftrightarrow & \color{red}{1197} x& = & 167 \\\Leftrightarrow & x = \frac{167}{1197} & & \\ & V = \left\{ \frac{167}{1197} \right\} & \\\end{align}\)