Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{7})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{-189x} +28 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+60} \\\Leftrightarrow & -420x+189x& = & 28+60 \\\Leftrightarrow & \color{red}{-231} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-231} & & \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{192}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 192x \color{red}{-160} & = & \color{red}{168x} +21 \\\Leftrightarrow & 192x \color{red}{-160} \color{blue}{+160} \color{blue}{-168x} & = & \color{red}{168x} +21 \color{blue}{-168x} \color{blue}{+160} \\\Leftrightarrow & 192x-168x& = & 21+160 \\\Leftrightarrow & \color{red}{24} x& = & 181 \\\Leftrightarrow & x = \frac{181}{24} & & \\ & V = \left\{ \frac{181}{24} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{25}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{75}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+75} & = & \color{red}{147x} +14 \\\Leftrightarrow & -210x \color{red}{+75} \color{blue}{-75} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-75} \\\Leftrightarrow & -210x-147x& = & 14-75 \\\Leftrightarrow & \color{red}{-357} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-357} & & \\\Leftrightarrow & x = \frac{61}{357} & & \\ & V = \left\{ \frac{61}{357} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{7})& = & -2x+\frac{7}{6} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{-84}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{+36} & = & \color{red}{-84x} +49 \\\Leftrightarrow & 630x \color{red}{+36} \color{blue}{-36} \color{blue}{+84x} & = & \color{red}{-84x} +49 \color{blue}{+84x} \color{blue}{-36} \\\Leftrightarrow & 630x+84x& = & 49-36 \\\Leftrightarrow & \color{red}{714} x& = & 13 \\\Leftrightarrow & x = \frac{13}{714} & & \\ & V = \left\{ \frac{13}{714} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+30} & = & \color{red}{49x} +5 \\\Leftrightarrow & 84x \color{red}{+30} \color{blue}{-30} \color{blue}{-49x} & = & \color{red}{49x} +5 \color{blue}{-49x} \color{blue}{-30} \\\Leftrightarrow & 84x-49x& = & 5-30 \\\Leftrightarrow & \color{red}{35} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{35} & & \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{16}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-48} & = & \color{red}{-165x} +110 \\\Leftrightarrow & 396x \color{red}{-48} \color{blue}{+48} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{+48} \\\Leftrightarrow & 396x+165x& = & 110+48 \\\Leftrightarrow & \color{red}{561} x& = & 158 \\\Leftrightarrow & x = \frac{158}{561} & & \\ & V = \left\{ \frac{158}{561} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{5})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 8x-\frac{8}{5}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x- \frac{8}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{-8} & = & \color{red}{25x} +8 \\\Leftrightarrow & 40x \color{red}{-8} \color{blue}{+8} \color{blue}{-25x} & = & \color{red}{25x} +8 \color{blue}{-25x} \color{blue}{+8} \\\Leftrightarrow & 40x-25x& = & 8+8 \\\Leftrightarrow & \color{red}{15} x& = & 16 \\\Leftrightarrow & x = \frac{16}{15} & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -35x+\frac{14}{3}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{+140} & = & \color{red}{-270x} +9 \\\Leftrightarrow & -1050x \color{red}{+140} \color{blue}{-140} \color{blue}{+270x} & = & \color{red}{-270x} +9 \color{blue}{+270x} \color{blue}{-140} \\\Leftrightarrow & -1050x+270x& = & 9-140 \\\Leftrightarrow & \color{red}{-780} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-780} & & \\\Leftrightarrow & x = \frac{131}{780} & & \\ & V = \left\{ \frac{131}{780} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 8x+\frac{16}{11}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+112} & = & \color{red}{-231x} +66 \\\Leftrightarrow & 616x \color{red}{+112} \color{blue}{-112} \color{blue}{+231x} & = & \color{red}{-231x} +66 \color{blue}{+231x} \color{blue}{-112} \\\Leftrightarrow & 616x+231x& = & 66-112 \\\Leftrightarrow & \color{red}{847} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{847} & & \\ & V = \left\{ \frac{-46}{847} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{8})& = & 4x+\frac{4}{9} \\\Leftrightarrow & -15x-\frac{15}{8}& = & 4x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1080}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{288}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1080x \color{red}{-135} & = & \color{red}{288x} +32 \\\Leftrightarrow & -1080x \color{red}{-135} \color{blue}{+135} \color{blue}{-288x} & = & \color{red}{288x} +32 \color{blue}{-288x} \color{blue}{+135} \\\Leftrightarrow & -1080x-288x& = & 32+135 \\\Leftrightarrow & \color{red}{-1368} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-1368} & & \\\Leftrightarrow & x = \frac{-167}{1368} & & \\ & V = \left\{ \frac{-167}{1368} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{3})& = & -2x+\frac{9}{8} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -2x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{+160} & = & \color{red}{-48x} +27 \\\Leftrightarrow & -600x \color{red}{+160} \color{blue}{-160} \color{blue}{+48x} & = & \color{red}{-48x} +27 \color{blue}{+48x} \color{blue}{-160} \\\Leftrightarrow & -600x+48x& = & 27-160 \\\Leftrightarrow & \color{red}{-552} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{-552} & & \\\Leftrightarrow & x = \frac{133}{552} & & \\ & V = \left\{ \frac{133}{552} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 6x+\frac{7}{3} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 6x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{18}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+14} & = & \color{red}{18x} +7 \\\Leftrightarrow & 105x \color{red}{+14} \color{blue}{-14} \color{blue}{-18x} & = & \color{red}{18x} +7 \color{blue}{-18x} \color{blue}{-14} \\\Leftrightarrow & 105x-18x& = & 7-14 \\\Leftrightarrow & \color{red}{87} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{87} & & \\ & V = \left\{ \frac{-7}{87} \right\} & \\\end{align}\)