Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{9})& = & -2x+\frac{5}{7} \\\Leftrightarrow & 21x+\frac{28}{9}& = & -2x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1323}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{-126}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1323x \color{red}{+196} & = & \color{red}{-126x} +45 \\\Leftrightarrow & 1323x \color{red}{+196} \color{blue}{-196} \color{blue}{+126x} & = & \color{red}{-126x} +45 \color{blue}{+126x} \color{blue}{-196} \\\Leftrightarrow & 1323x+126x& = & 45-196 \\\Leftrightarrow & \color{red}{1449} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{1449} & & \\ & V = \left\{ \frac{-151}{1449} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{12})& = & -9x+\frac{3}{5} \\\Leftrightarrow & -35x+\frac{35}{12}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-2100}{ \color{blue}{60} }x+ \frac{175}{ \color{blue}{60} })& = & (\frac{-540}{ \color{blue}{60} }x+ \frac{36}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -2100x \color{red}{+175} & = & \color{red}{-540x} +36 \\\Leftrightarrow & -2100x \color{red}{+175} \color{blue}{-175} \color{blue}{+540x} & = & \color{red}{-540x} +36 \color{blue}{+540x} \color{blue}{-175} \\\Leftrightarrow & -2100x+540x& = & 36-175 \\\Leftrightarrow & \color{red}{-1560} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-1560} & & \\\Leftrightarrow & x = \frac{139}{1560} & & \\ & V = \left\{ \frac{139}{1560} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{9}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{27}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-27} & = & \color{red}{147x} +56 \\\Leftrightarrow & 315x \color{red}{-27} \color{blue}{+27} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+27} \\\Leftrightarrow & 315x-147x& = & 56+27 \\\Leftrightarrow & \color{red}{168} x& = & 83 \\\Leftrightarrow & x = \frac{83}{168} & & \\ & V = \left\{ \frac{83}{168} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{-14} & = & \color{red}{-15x} +4 \\\Leftrightarrow & 84x \color{red}{-14} \color{blue}{+14} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{+14} \\\Leftrightarrow & 84x+15x& = & 4+14 \\\Leftrightarrow & \color{red}{99} x& = & 18 \\\Leftrightarrow & x = \frac{18}{99} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{11})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 28x+\frac{35}{11}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2156}{ \color{blue}{77} }x+ \frac{245}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2156x \color{red}{+245} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 2156x \color{red}{+245} \color{blue}{-245} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-245} \\\Leftrightarrow & 2156x+693x& = & 110-245 \\\Leftrightarrow & \color{red}{2849} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{2849} & & \\ & V = \left\{ \frac{-135}{2849} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{11})& = & 3x+\frac{3}{7} \\\Leftrightarrow & -8x+\frac{8}{11}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+56} & = & \color{red}{231x} +33 \\\Leftrightarrow & -616x \color{red}{+56} \color{blue}{-56} \color{blue}{-231x} & = & \color{red}{231x} +33 \color{blue}{-231x} \color{blue}{-56} \\\Leftrightarrow & -616x-231x& = & 33-56 \\\Leftrightarrow & \color{red}{-847} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-847} & & \\\Leftrightarrow & x = \frac{23}{847} & & \\ & V = \left\{ \frac{23}{847} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{5}{9} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+270} & = & \color{red}{315x} +35 \\\Leftrightarrow & -756x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & -756x-315x& = & 35-270 \\\Leftrightarrow & \color{red}{-1071} x& = & -235 \\\Leftrightarrow & x = \frac{-235}{-1071} & & \\\Leftrightarrow & x = \frac{235}{1071} & & \\ & V = \left\{ \frac{235}{1071} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{3})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 16x-\frac{16}{3}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x- \frac{176}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{-176} & = & \color{red}{-165x} +18 \\\Leftrightarrow & 528x \color{red}{-176} \color{blue}{+176} \color{blue}{+165x} & = & \color{red}{-165x} +18 \color{blue}{+165x} \color{blue}{+176} \\\Leftrightarrow & 528x+165x& = & 18+176 \\\Leftrightarrow & \color{red}{693} x& = & 194 \\\Leftrightarrow & x = \frac{194}{693} & & \\ & V = \left\{ \frac{194}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{3})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{-8} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{+8} \\\Leftrightarrow & 24x+27x& = & 8+8 \\\Leftrightarrow & \color{red}{51} x& = & 16 \\\Leftrightarrow & x = \frac{16}{51} & & \\ & V = \left\{ \frac{16}{51} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-150} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 420x \color{red}{-150} \color{blue}{+150} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+150} \\\Leftrightarrow & 420x+175x& = & 42+150 \\\Leftrightarrow & \color{red}{595} x& = & 192 \\\Leftrightarrow & x = \frac{192}{595} & & \\ & V = \left\{ \frac{192}{595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{30}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-90} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 594x \color{red}{-90} \color{blue}{+90} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+90} \\\Leftrightarrow & 594x+231x& = & 44+90 \\\Leftrightarrow & \color{red}{825} x& = & 134 \\\Leftrightarrow & x = \frac{134}{825} & & \\ & V = \left\{ \frac{134}{825} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -8x-\frac{16}{7}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{-16} & = & \color{red}{21x} +4 \\\Leftrightarrow & -56x \color{red}{-16} \color{blue}{+16} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+16} \\\Leftrightarrow & -56x-21x& = & 4+16 \\\Leftrightarrow & \color{red}{-77} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-77} & & \\\Leftrightarrow & x = \frac{-20}{77} & & \\ & V = \left\{ \frac{-20}{77} \right\} & \\\end{align}\)