Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{10})& = & -9x+\frac{8}{7} \\\Leftrightarrow & -28x-\frac{21}{10}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1960}{ \color{blue}{70} }x- \frac{147}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{80}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1960x \color{red}{-147} & = & \color{red}{-630x} +80 \\\Leftrightarrow & -1960x \color{red}{-147} \color{blue}{+147} \color{blue}{+630x} & = & \color{red}{-630x} +80 \color{blue}{+630x} \color{blue}{+147} \\\Leftrightarrow & -1960x+630x& = & 80+147 \\\Leftrightarrow & \color{red}{-1330} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-1330} & & \\\Leftrightarrow & x = \frac{-227}{1330} & & \\ & V = \left\{ \frac{-227}{1330} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{8})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -20x-\frac{15}{8}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-160}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -160x \color{red}{-15} & = & \color{red}{56x} +18 \\\Leftrightarrow & -160x \color{red}{-15} \color{blue}{+15} \color{blue}{-56x} & = & \color{red}{56x} +18 \color{blue}{-56x} \color{blue}{+15} \\\Leftrightarrow & -160x-56x& = & 18+15 \\\Leftrightarrow & \color{red}{-216} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-216} & & \\\Leftrightarrow & x = \frac{-11}{72} & & \\ & V = \left\{ \frac{-11}{72} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{5})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{275x} +20 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +20 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -660x-275x& = & 20+132 \\\Leftrightarrow & \color{red}{-935} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-935} & & \\\Leftrightarrow & x = \frac{-152}{935} & & \\ & V = \left\{ \frac{-152}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{+165} & = & \color{red}{-396x} +40 \\\Leftrightarrow & 1100x \color{red}{+165} \color{blue}{-165} \color{blue}{+396x} & = & \color{red}{-396x} +40 \color{blue}{+396x} \color{blue}{-165} \\\Leftrightarrow & 1100x+396x& = & 40-165 \\\Leftrightarrow & \color{red}{1496} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{1496} & & \\ & V = \left\{ \frac{-125}{1496} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{9})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+40} & = & \color{red}{405x} +36 \\\Leftrightarrow & -360x \color{red}{+40} \color{blue}{-40} \color{blue}{-405x} & = & \color{red}{405x} +36 \color{blue}{-405x} \color{blue}{-40} \\\Leftrightarrow & -360x-405x& = & 36-40 \\\Leftrightarrow & \color{red}{-765} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-765} & & \\\Leftrightarrow & x = \frac{4}{765} & & \\ & V = \left\{ \frac{4}{765} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 12x+\frac{16}{3}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x+ \frac{32}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{+32} & = & \color{red}{-30x} +5 \\\Leftrightarrow & 72x \color{red}{+32} \color{blue}{-32} \color{blue}{+30x} & = & \color{red}{-30x} +5 \color{blue}{+30x} \color{blue}{-32} \\\Leftrightarrow & 72x+30x& = & 5-32 \\\Leftrightarrow & \color{red}{102} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{102} & & \\\Leftrightarrow & x = \frac{-9}{34} & & \\ & V = \left\{ \frac{-9}{34} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{11})& = & 4x+\frac{9}{10} \\\Leftrightarrow & -15x-\frac{10}{11}& = & 4x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x- \frac{100}{ \color{blue}{110} })& = & (\frac{440}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{-100} & = & \color{red}{440x} +99 \\\Leftrightarrow & -1650x \color{red}{-100} \color{blue}{+100} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{+100} \\\Leftrightarrow & -1650x-440x& = & 99+100 \\\Leftrightarrow & \color{red}{-2090} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-2090} & & \\\Leftrightarrow & x = \frac{-199}{2090} & & \\ & V = \left\{ \frac{-199}{2090} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{9})& = & -8x+\frac{4}{11} \\\Leftrightarrow & 21x-\frac{28}{9}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{-308} & = & \color{red}{-792x} +36 \\\Leftrightarrow & 2079x \color{red}{-308} \color{blue}{+308} \color{blue}{+792x} & = & \color{red}{-792x} +36 \color{blue}{+792x} \color{blue}{+308} \\\Leftrightarrow & 2079x+792x& = & 36+308 \\\Leftrightarrow & \color{red}{2871} x& = & 344 \\\Leftrightarrow & x = \frac{344}{2871} & & \\ & V = \left\{ \frac{344}{2871} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{5})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x+\frac{8}{5}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+16} & = & \color{red}{-70x} +25 \\\Leftrightarrow & -60x \color{red}{+16} \color{blue}{-16} \color{blue}{+70x} & = & \color{red}{-70x} +25 \color{blue}{+70x} \color{blue}{-16} \\\Leftrightarrow & -60x+70x& = & 25-16 \\\Leftrightarrow & \color{red}{10} x& = & 9 \\\Leftrightarrow & x = \frac{9}{10} & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-6} & = & \color{red}{-49x} +6 \\\Leftrightarrow & 84x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +6 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & 84x+49x& = & 6+6 \\\Leftrightarrow & \color{red}{133} x& = & 12 \\\Leftrightarrow & x = \frac{12}{133} & & \\ & V = \left\{ \frac{12}{133} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{8})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -21x-\frac{35}{8}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x- \frac{385}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{-385} & = & \color{red}{704x} +48 \\\Leftrightarrow & -1848x \color{red}{-385} \color{blue}{+385} \color{blue}{-704x} & = & \color{red}{704x} +48 \color{blue}{-704x} \color{blue}{+385} \\\Leftrightarrow & -1848x-704x& = & 48+385 \\\Leftrightarrow & \color{red}{-2552} x& = & 433 \\\Leftrightarrow & x = \frac{433}{-2552} & & \\\Leftrightarrow & x = \frac{-433}{2552} & & \\ & V = \left\{ \frac{-433}{2552} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{5})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{9}{5}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-99} & = & \color{red}{-385x} +25 \\\Leftrightarrow & -330x \color{red}{-99} \color{blue}{+99} \color{blue}{+385x} & = & \color{red}{-385x} +25 \color{blue}{+385x} \color{blue}{+99} \\\Leftrightarrow & -330x+385x& = & 25+99 \\\Leftrightarrow & \color{red}{55} x& = & 124 \\\Leftrightarrow & x = \frac{124}{55} & & \\ & V = \left\{ \frac{124}{55} \right\} & \\\end{align}\)