Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{5})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 4x+\frac{8}{5}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{+16} & = & \color{red}{30x} +45 \\\Leftrightarrow & 40x \color{red}{+16} \color{blue}{-16} \color{blue}{-30x} & = & \color{red}{30x} +45 \color{blue}{-30x} \color{blue}{-16} \\\Leftrightarrow & 40x-30x& = & 45-16 \\\Leftrightarrow & \color{red}{10} x& = & 29 \\\Leftrightarrow & x = \frac{29}{10} & & \\ & V = \left\{ \frac{29}{10} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{7})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -24x-\frac{18}{7}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{198}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-198} & = & \color{red}{385x} +70 \\\Leftrightarrow & -1848x \color{red}{-198} \color{blue}{+198} \color{blue}{-385x} & = & \color{red}{385x} +70 \color{blue}{-385x} \color{blue}{+198} \\\Leftrightarrow & -1848x-385x& = & 70+198 \\\Leftrightarrow & \color{red}{-2233} x& = & 268 \\\Leftrightarrow & x = \frac{268}{-2233} & & \\\Leftrightarrow & x = \frac{-268}{2233} & & \\ & V = \left\{ \frac{-268}{2233} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-8} & = & \color{red}{-63x} +4 \\\Leftrightarrow & 72x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & 72x+63x& = & 4+8 \\\Leftrightarrow & \color{red}{135} x& = & 12 \\\Leftrightarrow & x = \frac{12}{135} & & \\\Leftrightarrow & x = \frac{4}{45} & & \\ & V = \left\{ \frac{4}{45} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -7x+\frac{3}{8} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+21} & = & \color{red}{-56x} +3 \\\Leftrightarrow & -224x \color{red}{+21} \color{blue}{-21} \color{blue}{+56x} & = & \color{red}{-56x} +3 \color{blue}{+56x} \color{blue}{-21} \\\Leftrightarrow & -224x+56x& = & 3-21 \\\Leftrightarrow & \color{red}{-168} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-168} & & \\\Leftrightarrow & x = \frac{3}{28} & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{9})& = & 5x+\frac{7}{10} \\\Leftrightarrow & 14x-\frac{28}{9}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1260}{ \color{blue}{90} }x- \frac{280}{ \color{blue}{90} })& = & (\frac{450}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1260x \color{red}{-280} & = & \color{red}{450x} +63 \\\Leftrightarrow & 1260x \color{red}{-280} \color{blue}{+280} \color{blue}{-450x} & = & \color{red}{450x} +63 \color{blue}{-450x} \color{blue}{+280} \\\Leftrightarrow & 1260x-450x& = & 63+280 \\\Leftrightarrow & \color{red}{810} x& = & 343 \\\Leftrightarrow & x = \frac{343}{810} & & \\ & V = \left\{ \frac{343}{810} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{9})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 20x-\frac{25}{9}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x- \frac{125}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{-125} & = & \color{red}{-315x} +18 \\\Leftrightarrow & 900x \color{red}{-125} \color{blue}{+125} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{+125} \\\Leftrightarrow & 900x+315x& = & 18+125 \\\Leftrightarrow & \color{red}{1215} x& = & 143 \\\Leftrightarrow & x = \frac{143}{1215} & & \\ & V = \left\{ \frac{143}{1215} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{11})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-50} & = & \color{red}{165x} +66 \\\Leftrightarrow & 550x \color{red}{-50} \color{blue}{+50} \color{blue}{-165x} & = & \color{red}{165x} +66 \color{blue}{-165x} \color{blue}{+50} \\\Leftrightarrow & 550x-165x& = & 66+50 \\\Leftrightarrow & \color{red}{385} x& = & 116 \\\Leftrightarrow & x = \frac{116}{385} & & \\ & V = \left\{ \frac{116}{385} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{3})& = & -9x+\frac{3}{10} \\\Leftrightarrow & 10x+\frac{10}{3}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x+ \frac{100}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{+100} & = & \color{red}{-270x} +9 \\\Leftrightarrow & 300x \color{red}{+100} \color{blue}{-100} \color{blue}{+270x} & = & \color{red}{-270x} +9 \color{blue}{+270x} \color{blue}{-100} \\\Leftrightarrow & 300x+270x& = & 9-100 \\\Leftrightarrow & \color{red}{570} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{570} & & \\ & V = \left\{ \frac{-91}{570} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{11})& = & 9x+\frac{3}{4} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-40} & = & \color{red}{396x} +33 \\\Leftrightarrow & 440x \color{red}{-40} \color{blue}{+40} \color{blue}{-396x} & = & \color{red}{396x} +33 \color{blue}{-396x} \color{blue}{+40} \\\Leftrightarrow & 440x-396x& = & 33+40 \\\Leftrightarrow & \color{red}{44} x& = & 73 \\\Leftrightarrow & x = \frac{73}{44} & & \\ & V = \left\{ \frac{73}{44} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{11})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1584}{ \color{blue}{66} }x- \frac{180}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1584x \color{red}{-180} & = & \color{red}{330x} +55 \\\Leftrightarrow & 1584x \color{red}{-180} \color{blue}{+180} \color{blue}{-330x} & = & \color{red}{330x} +55 \color{blue}{-330x} \color{blue}{+180} \\\Leftrightarrow & 1584x-330x& = & 55+180 \\\Leftrightarrow & \color{red}{1254} x& = & 235 \\\Leftrightarrow & x = \frac{235}{1254} & & \\ & V = \left\{ \frac{235}{1254} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{7})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -16x+\frac{12}{7}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-448}{ \color{blue}{28} }x+ \frac{48}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -448x \color{red}{+48} & = & \color{red}{196x} +35 \\\Leftrightarrow & -448x \color{red}{+48} \color{blue}{-48} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{-48} \\\Leftrightarrow & -448x-196x& = & 35-48 \\\Leftrightarrow & \color{red}{-644} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-644} & & \\\Leftrightarrow & x = \frac{13}{644} & & \\ & V = \left\{ \frac{13}{644} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{3})& = & 4x+\frac{5}{11} \\\Leftrightarrow & 21x-\frac{35}{3}& = & 4x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{385}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-385} & = & \color{red}{132x} +15 \\\Leftrightarrow & 693x \color{red}{-385} \color{blue}{+385} \color{blue}{-132x} & = & \color{red}{132x} +15 \color{blue}{-132x} \color{blue}{+385} \\\Leftrightarrow & 693x-132x& = & 15+385 \\\Leftrightarrow & \color{red}{561} x& = & 400 \\\Leftrightarrow & x = \frac{400}{561} & & \\ & V = \left\{ \frac{400}{561} \right\} & \\\end{align}\)