Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{9})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{10}{9}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{135}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 135x \color{red}{+10} & = & \color{red}{-63x} +24 \\\Leftrightarrow & 135x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +24 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & 135x+63x& = & 24-10 \\\Leftrightarrow & \color{red}{198} x& = & 14 \\\Leftrightarrow & x = \frac{14}{198} & & \\\Leftrightarrow & x = \frac{7}{99} & & \\ & V = \left\{ \frac{7}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 30x-\frac{24}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1200}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1200x \color{red}{-192} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 1200x \color{red}{-192} \color{blue}{+192} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+192} \\\Leftrightarrow & 1200x+280x& = & 35+192 \\\Leftrightarrow & \color{red}{1480} x& = & 227 \\\Leftrightarrow & x = \frac{227}{1480} & & \\ & V = \left\{ \frac{227}{1480} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+6} & = & \color{red}{-49x} +3 \\\Leftrightarrow & 70x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & 70x+49x& = & 3-6 \\\Leftrightarrow & \color{red}{119} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{119} & & \\ & V = \left\{ \frac{-3}{119} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 24x+\frac{24}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+168} & = & \color{red}{385x} +110 \\\Leftrightarrow & 1848x \color{red}{+168} \color{blue}{-168} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{-168} \\\Leftrightarrow & 1848x-385x& = & 110-168 \\\Leftrightarrow & \color{red}{1463} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{1463} & & \\ & V = \left\{ \frac{-58}{1463} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{5}{4} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{-72} & = & \color{red}{308x} +55 \\\Leftrightarrow & 1320x \color{red}{-72} \color{blue}{+72} \color{blue}{-308x} & = & \color{red}{308x} +55 \color{blue}{-308x} \color{blue}{+72} \\\Leftrightarrow & 1320x-308x& = & 55+72 \\\Leftrightarrow & \color{red}{1012} x& = & 127 \\\Leftrightarrow & x = \frac{127}{1012} & & \\ & V = \left\{ \frac{127}{1012} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 4x+\frac{4}{11} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 4x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-154} & = & \color{red}{132x} +12 \\\Leftrightarrow & -1155x \color{red}{-154} \color{blue}{+154} \color{blue}{-132x} & = & \color{red}{132x} +12 \color{blue}{-132x} \color{blue}{+154} \\\Leftrightarrow & -1155x-132x& = & 12+154 \\\Leftrightarrow & \color{red}{-1287} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-1287} & & \\\Leftrightarrow & x = \frac{-166}{1287} & & \\ & V = \left\{ \frac{-166}{1287} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{9})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -4x+\frac{10}{9}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{+70} & = & \color{red}{-315x} +81 \\\Leftrightarrow & -252x \color{red}{+70} \color{blue}{-70} \color{blue}{+315x} & = & \color{red}{-315x} +81 \color{blue}{+315x} \color{blue}{-70} \\\Leftrightarrow & -252x+315x& = & 81-70 \\\Leftrightarrow & \color{red}{63} x& = & 11 \\\Leftrightarrow & x = \frac{11}{63} & & \\ & V = \left\{ \frac{11}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{5})& = & 3x+\frac{5}{4} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{+48} & = & \color{red}{60x} +25 \\\Leftrightarrow & -400x \color{red}{+48} \color{blue}{-48} \color{blue}{-60x} & = & \color{red}{60x} +25 \color{blue}{-60x} \color{blue}{-48} \\\Leftrightarrow & -400x-60x& = & 25-48 \\\Leftrightarrow & \color{red}{-460} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-460} & & \\\Leftrightarrow & x = \frac{1}{20} & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{6})& = & 9x+\frac{3}{11} \\\Leftrightarrow & -35x+\frac{35}{6}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-2310}{ \color{blue}{66} }x+ \frac{385}{ \color{blue}{66} })& = & (\frac{594}{ \color{blue}{66} }x+ \frac{18}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -2310x \color{red}{+385} & = & \color{red}{594x} +18 \\\Leftrightarrow & -2310x \color{red}{+385} \color{blue}{-385} \color{blue}{-594x} & = & \color{red}{594x} +18 \color{blue}{-594x} \color{blue}{-385} \\\Leftrightarrow & -2310x-594x& = & 18-385 \\\Leftrightarrow & \color{red}{-2904} x& = & -367 \\\Leftrightarrow & x = \frac{-367}{-2904} & & \\\Leftrightarrow & x = \frac{367}{2904} & & \\ & V = \left\{ \frac{367}{2904} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 24x-\frac{24}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-264} & = & \color{red}{-275x} +50 \\\Leftrightarrow & 1320x \color{red}{-264} \color{blue}{+264} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{+264} \\\Leftrightarrow & 1320x+275x& = & 50+264 \\\Leftrightarrow & \color{red}{1595} x& = & 314 \\\Leftrightarrow & x = \frac{314}{1595} & & \\ & V = \left\{ \frac{314}{1595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{11})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 15x+\frac{20}{11}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+60} & = & \color{red}{66x} +22 \\\Leftrightarrow & 495x \color{red}{+60} \color{blue}{-60} \color{blue}{-66x} & = & \color{red}{66x} +22 \color{blue}{-66x} \color{blue}{-60} \\\Leftrightarrow & 495x-66x& = & 22-60 \\\Leftrightarrow & \color{red}{429} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{429} & & \\ & V = \left\{ \frac{-38}{429} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{9})& = & 3x+\frac{7}{3} \\\Leftrightarrow & 25x-\frac{10}{9}& = & 3x+\frac{7}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{21}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{-10} & = & \color{red}{27x} +21 \\\Leftrightarrow & 225x \color{red}{-10} \color{blue}{+10} \color{blue}{-27x} & = & \color{red}{27x} +21 \color{blue}{-27x} \color{blue}{+10} \\\Leftrightarrow & 225x-27x& = & 21+10 \\\Leftrightarrow & \color{red}{198} x& = & 31 \\\Leftrightarrow & x = \frac{31}{198} & & \\ & V = \left\{ \frac{31}{198} \right\} & \\\end{align}\)