Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{-110x} +33 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-36} \\\Leftrightarrow & 396x+110x& = & 33-36 \\\Leftrightarrow & \color{red}{506} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{506} & & \\ & V = \left\{ \frac{-3}{506} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-66} & = & \color{red}{539x} +56 \\\Leftrightarrow & 1155x \color{red}{-66} \color{blue}{+66} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{+66} \\\Leftrightarrow & 1155x-539x& = & 56+66 \\\Leftrightarrow & \color{red}{616} x& = & 122 \\\Leftrightarrow & x = \frac{122}{616} & & \\\Leftrightarrow & x = \frac{61}{308} & & \\ & V = \left\{ \frac{61}{308} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+8} & = & \color{red}{-81x} +6 \\\Leftrightarrow & -72x \color{red}{+8} \color{blue}{-8} \color{blue}{+81x} & = & \color{red}{-81x} +6 \color{blue}{+81x} \color{blue}{-8} \\\Leftrightarrow & -72x+81x& = & 6-8 \\\Leftrightarrow & \color{red}{9} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{1}{2})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -25x-\frac{5}{2}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-50}{ \color{blue}{2} }x- \frac{5}{ \color{blue}{2} })& = & (\frac{16}{ \color{blue}{2} }x+ \frac{7}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -50x \color{red}{-5} & = & \color{red}{16x} +7 \\\Leftrightarrow & -50x \color{red}{-5} \color{blue}{+5} \color{blue}{-16x} & = & \color{red}{16x} +7 \color{blue}{-16x} \color{blue}{+5} \\\Leftrightarrow & -50x-16x& = & 7+5 \\\Leftrightarrow & \color{red}{-66} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-66} & & \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{9})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 6x-\frac{8}{9}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{216}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 216x \color{red}{-32} & = & \color{red}{180x} +27 \\\Leftrightarrow & 216x \color{red}{-32} \color{blue}{+32} \color{blue}{-180x} & = & \color{red}{180x} +27 \color{blue}{-180x} \color{blue}{+32} \\\Leftrightarrow & 216x-180x& = & 27+32 \\\Leftrightarrow & \color{red}{36} x& = & 59 \\\Leftrightarrow & x = \frac{59}{36} & & \\ & V = \left\{ \frac{59}{36} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{3})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 25x+\frac{25}{3}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x+ \frac{50}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{+50} & = & \color{red}{-42x} +27 \\\Leftrightarrow & 150x \color{red}{+50} \color{blue}{-50} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{-50} \\\Leftrightarrow & 150x+42x& = & 27-50 \\\Leftrightarrow & \color{red}{192} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{192} & & \\ & V = \left\{ \frac{-23}{192} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & -6x+\frac{3}{5} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -6x+\frac{3}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-240}{ \color{blue}{40} }x+ \frac{24}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+105} & = & \color{red}{-240x} +24 \\\Leftrightarrow & -1400x \color{red}{+105} \color{blue}{-105} \color{blue}{+240x} & = & \color{red}{-240x} +24 \color{blue}{+240x} \color{blue}{-105} \\\Leftrightarrow & -1400x+240x& = & 24-105 \\\Leftrightarrow & \color{red}{-1160} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-1160} & & \\\Leftrightarrow & x = \frac{81}{1160} & & \\ & V = \left\{ \frac{81}{1160} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{11})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -9x+\frac{9}{11}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x+ \frac{72}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{+72} & = & \color{red}{440x} +77 \\\Leftrightarrow & -792x \color{red}{+72} \color{blue}{-72} \color{blue}{-440x} & = & \color{red}{440x} +77 \color{blue}{-440x} \color{blue}{-72} \\\Leftrightarrow & -792x-440x& = & 77-72 \\\Leftrightarrow & \color{red}{-1232} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-1232} & & \\\Leftrightarrow & x = \frac{-5}{1232} & & \\ & V = \left\{ \frac{-5}{1232} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & -2x+\frac{9}{11} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -2x+\frac{9}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{-176}{ \color{blue}{88} }x+ \frac{72}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+165} & = & \color{red}{-176x} +72 \\\Leftrightarrow & 1320x \color{red}{+165} \color{blue}{-165} \color{blue}{+176x} & = & \color{red}{-176x} +72 \color{blue}{+176x} \color{blue}{-165} \\\Leftrightarrow & 1320x+176x& = & 72-165 \\\Leftrightarrow & \color{red}{1496} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{1496} & & \\ & V = \left\{ \frac{-93}{1496} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 16x-\frac{8}{3}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{-40} & = & \color{red}{45x} +12 \\\Leftrightarrow & 240x \color{red}{-40} \color{blue}{+40} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{+40} \\\Leftrightarrow & 240x-45x& = & 12+40 \\\Leftrightarrow & \color{red}{195} x& = & 52 \\\Leftrightarrow & x = \frac{52}{195} & & \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-10}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{-12} & = & \color{red}{-10x} +6 \\\Leftrightarrow & 45x \color{red}{-12} \color{blue}{+12} \color{blue}{+10x} & = & \color{red}{-10x} +6 \color{blue}{+10x} \color{blue}{+12} \\\Leftrightarrow & 45x+10x& = & 6+12 \\\Leftrightarrow & \color{red}{55} x& = & 18 \\\Leftrightarrow & x = \frac{18}{55} & & \\ & V = \left\{ \frac{18}{55} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{8})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{15}{8}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{144}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 144x \color{red}{-45} & = & \color{red}{-120x} +64 \\\Leftrightarrow & 144x \color{red}{-45} \color{blue}{+45} \color{blue}{+120x} & = & \color{red}{-120x} +64 \color{blue}{+120x} \color{blue}{+45} \\\Leftrightarrow & 144x+120x& = & 64+45 \\\Leftrightarrow & \color{red}{264} x& = & 109 \\\Leftrightarrow & x = \frac{109}{264} & & \\ & V = \left\{ \frac{109}{264} \right\} & \\\end{align}\)