Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -8x+\frac{8}{3} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{-14} & = & \color{red}{-24x} +8 \\\Leftrightarrow & 63x \color{red}{-14} \color{blue}{+14} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{+14} \\\Leftrightarrow & 63x+24x& = & 8+14 \\\Leftrightarrow & \color{red}{87} x& = & 22 \\\Leftrightarrow & x = \frac{22}{87} & & \\ & V = \left\{ \frac{22}{87} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 8x+\frac{16}{7}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{672}{ \color{blue}{84} }x+ \frac{192}{ \color{blue}{84} })& = & (\frac{-252}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 672x \color{red}{+192} & = & \color{red}{-252x} +35 \\\Leftrightarrow & 672x \color{red}{+192} \color{blue}{-192} \color{blue}{+252x} & = & \color{red}{-252x} +35 \color{blue}{+252x} \color{blue}{-192} \\\Leftrightarrow & 672x+252x& = & 35-192 \\\Leftrightarrow & \color{red}{924} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{924} & & \\ & V = \left\{ \frac{-157}{924} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{11})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 16x-\frac{8}{11}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{-8} & = & \color{red}{77x} +10 \\\Leftrightarrow & 176x \color{red}{-8} \color{blue}{+8} \color{blue}{-77x} & = & \color{red}{77x} +10 \color{blue}{-77x} \color{blue}{+8} \\\Leftrightarrow & 176x-77x& = & 10+8 \\\Leftrightarrow & \color{red}{99} x& = & 18 \\\Leftrightarrow & x = \frac{18}{99} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{11})& = & 3x+\frac{8}{7} \\\Leftrightarrow & 8x-\frac{6}{11}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-42} & = & \color{red}{231x} +88 \\\Leftrightarrow & 616x \color{red}{-42} \color{blue}{+42} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{+42} \\\Leftrightarrow & 616x-231x& = & 88+42 \\\Leftrightarrow & \color{red}{385} x& = & 130 \\\Leftrightarrow & x = \frac{130}{385} & & \\\Leftrightarrow & x = \frac{26}{77} & & \\ & V = \left\{ \frac{26}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{-275x} +10 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & -660x+275x& = & 10+132 \\\Leftrightarrow & \color{red}{-385} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-385} & & \\\Leftrightarrow & x = \frac{-142}{385} & & \\ & V = \left\{ \frac{-142}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{11})& = & -2x+\frac{5}{12} \\\Leftrightarrow & 9x+\frac{12}{11}& = & -2x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1188}{ \color{blue}{132} }x+ \frac{144}{ \color{blue}{132} })& = & (\frac{-264}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1188x \color{red}{+144} & = & \color{red}{-264x} +55 \\\Leftrightarrow & 1188x \color{red}{+144} \color{blue}{-144} \color{blue}{+264x} & = & \color{red}{-264x} +55 \color{blue}{+264x} \color{blue}{-144} \\\Leftrightarrow & 1188x+264x& = & 55-144 \\\Leftrightarrow & \color{red}{1452} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{1452} & & \\ & V = \left\{ \frac{-89}{1452} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{7})& = & -9x+\frac{7}{4} \\\Leftrightarrow & -18x+\frac{12}{7}& = & -9x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-504}{ \color{blue}{28} }x+ \frac{48}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -504x \color{red}{+48} & = & \color{red}{-252x} +49 \\\Leftrightarrow & -504x \color{red}{+48} \color{blue}{-48} \color{blue}{+252x} & = & \color{red}{-252x} +49 \color{blue}{+252x} \color{blue}{-48} \\\Leftrightarrow & -504x+252x& = & 49-48 \\\Leftrightarrow & \color{red}{-252} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-252} & & \\\Leftrightarrow & x = \frac{-1}{252} & & \\ & V = \left\{ \frac{-1}{252} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -4x-\frac{10}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{-30} & = & \color{red}{-165x} +110 \\\Leftrightarrow & -132x \color{red}{-30} \color{blue}{+30} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{+30} \\\Leftrightarrow & -132x+165x& = & 110+30 \\\Leftrightarrow & \color{red}{33} x& = & 140 \\\Leftrightarrow & x = \frac{140}{33} & & \\ & V = \left\{ \frac{140}{33} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{56}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{+45} & = & \color{red}{120x} +56 \\\Leftrightarrow & 288x \color{red}{+45} \color{blue}{-45} \color{blue}{-120x} & = & \color{red}{120x} +56 \color{blue}{-120x} \color{blue}{-45} \\\Leftrightarrow & 288x-120x& = & 56-45 \\\Leftrightarrow & \color{red}{168} x& = & 11 \\\Leftrightarrow & x = \frac{11}{168} & & \\ & V = \left\{ \frac{11}{168} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{7})& = & -3x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{-42x} +21 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{+40} \\\Leftrightarrow & -280x+42x& = & 21+40 \\\Leftrightarrow & \color{red}{-238} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-238} & & \\\Leftrightarrow & x = \frac{-61}{238} & & \\ & V = \left\{ \frac{-61}{238} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{112}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 112x \color{red}{+24} & = & \color{red}{196x} +21 \\\Leftrightarrow & 112x \color{red}{+24} \color{blue}{-24} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-24} \\\Leftrightarrow & 112x-196x& = & 21-24 \\\Leftrightarrow & \color{red}{-84} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-84} & & \\\Leftrightarrow & x = \frac{1}{28} & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{2})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{15}{2}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+105} & = & \color{red}{-98x} +20 \\\Leftrightarrow & 210x \color{red}{+105} \color{blue}{-105} \color{blue}{+98x} & = & \color{red}{-98x} +20 \color{blue}{+98x} \color{blue}{-105} \\\Leftrightarrow & 210x+98x& = & 20-105 \\\Leftrightarrow & \color{red}{308} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{308} & & \\ & V = \left\{ \frac{-85}{308} \right\} & \\\end{align}\)