Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{7})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{20}{7}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-160} & = & \color{red}{280x} +49 \\\Leftrightarrow & 672x \color{red}{-160} \color{blue}{+160} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{+160} \\\Leftrightarrow & 672x-280x& = & 49+160 \\\Leftrightarrow & \color{red}{392} x& = & 209 \\\Leftrightarrow & x = \frac{209}{392} & & \\ & V = \left\{ \frac{209}{392} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -10x+\frac{20}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+100} & = & \color{red}{-245x} +21 \\\Leftrightarrow & -350x \color{red}{+100} \color{blue}{-100} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{-100} \\\Leftrightarrow & -350x+245x& = & 21-100 \\\Leftrightarrow & \color{red}{-105} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-105} & & \\\Leftrightarrow & x = \frac{79}{105} & & \\ & V = \left\{ \frac{79}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{147x} +14 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & -126x-147x& = & 14-30 \\\Leftrightarrow & \color{red}{-273} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-273} & & \\\Leftrightarrow & x = \frac{16}{273} & & \\ & V = \left\{ \frac{16}{273} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{11})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 14x-\frac{35}{11}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1232}{ \color{blue}{88} }x- \frac{280}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1232x \color{red}{-280} & = & \color{red}{264x} +77 \\\Leftrightarrow & 1232x \color{red}{-280} \color{blue}{+280} \color{blue}{-264x} & = & \color{red}{264x} +77 \color{blue}{-264x} \color{blue}{+280} \\\Leftrightarrow & 1232x-264x& = & 77+280 \\\Leftrightarrow & \color{red}{968} x& = & 357 \\\Leftrightarrow & x = \frac{357}{968} & & \\ & V = \left\{ \frac{357}{968} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{9})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -28x-\frac{35}{9}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-385} & = & \color{red}{495x} +36 \\\Leftrightarrow & -2772x \color{red}{-385} \color{blue}{+385} \color{blue}{-495x} & = & \color{red}{495x} +36 \color{blue}{-495x} \color{blue}{+385} \\\Leftrightarrow & -2772x-495x& = & 36+385 \\\Leftrightarrow & \color{red}{-3267} x& = & 421 \\\Leftrightarrow & x = \frac{421}{-3267} & & \\\Leftrightarrow & x = \frac{-421}{3267} & & \\ & V = \left\{ \frac{-421}{3267} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-6} & = & \color{red}{49x} +2 \\\Leftrightarrow & -63x \color{red}{-6} \color{blue}{+6} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{+6} \\\Leftrightarrow & -63x-49x& = & 2+6 \\\Leftrightarrow & \color{red}{-112} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-112} & & \\\Leftrightarrow & x = \frac{-1}{14} & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{+12} & = & \color{red}{35x} +2 \\\Leftrightarrow & -150x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & -150x-35x& = & 2-12 \\\Leftrightarrow & \color{red}{-185} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-185} & & \\\Leftrightarrow & x = \frac{2}{37} & & \\ & V = \left\{ \frac{2}{37} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+50} & = & \color{red}{-315x} +42 \\\Leftrightarrow & -700x \color{red}{+50} \color{blue}{-50} \color{blue}{+315x} & = & \color{red}{-315x} +42 \color{blue}{+315x} \color{blue}{-50} \\\Leftrightarrow & -700x+315x& = & 42-50 \\\Leftrightarrow & \color{red}{-385} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-385} & & \\\Leftrightarrow & x = \frac{8}{385} & & \\ & V = \left\{ \frac{8}{385} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{12})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -10x-\frac{25}{12}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 12 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x- \frac{50}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{-50} & = & \color{red}{-168x} +21 \\\Leftrightarrow & -240x \color{red}{-50} \color{blue}{+50} \color{blue}{+168x} & = & \color{red}{-168x} +21 \color{blue}{+168x} \color{blue}{+50} \\\Leftrightarrow & -240x+168x& = & 21+50 \\\Leftrightarrow & \color{red}{-72} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-72} & & \\\Leftrightarrow & x = \frac{-71}{72} & & \\ & V = \left\{ \frac{-71}{72} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{9})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -14x+\frac{35}{9}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{+35} & = & \color{red}{-27x} +24 \\\Leftrightarrow & -126x \color{red}{+35} \color{blue}{-35} \color{blue}{+27x} & = & \color{red}{-27x} +24 \color{blue}{+27x} \color{blue}{-35} \\\Leftrightarrow & -126x+27x& = & 24-35 \\\Leftrightarrow & \color{red}{-99} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-99} & & \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{7})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 6x-\frac{9}{7}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{45}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-45} & = & \color{red}{175x} +28 \\\Leftrightarrow & 210x \color{red}{-45} \color{blue}{+45} \color{blue}{-175x} & = & \color{red}{175x} +28 \color{blue}{-175x} \color{blue}{+45} \\\Leftrightarrow & 210x-175x& = & 28+45 \\\Leftrightarrow & \color{red}{35} x& = & 73 \\\Leftrightarrow & x = \frac{73}{35} & & \\ & V = \left\{ \frac{73}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{8})& = & 6x+\frac{7}{8} \\\Leftrightarrow & -28x+\frac{35}{8}& = & 6x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{35}{ \color{blue}{8} })& = & (\frac{48}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+35} & = & \color{red}{48x} +7 \\\Leftrightarrow & -224x \color{red}{+35} \color{blue}{-35} \color{blue}{-48x} & = & \color{red}{48x} +7 \color{blue}{-48x} \color{blue}{-35} \\\Leftrightarrow & -224x-48x& = & 7-35 \\\Leftrightarrow & \color{red}{-272} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-272} & & \\\Leftrightarrow & x = \frac{7}{68} & & \\ & V = \left\{ \frac{7}{68} \right\} & \\\end{align}\)