Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -9x+\frac{6}{7}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{+6} & = & \color{red}{-35x} +5 \\\Leftrightarrow & -63x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +5 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & -63x+35x& = & 5-6 \\\Leftrightarrow & \color{red}{-28} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-28} & & \\\Leftrightarrow & x = \frac{1}{28} & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{8}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+8} & = & \color{red}{-27x} +4 \\\Leftrightarrow & 60x \color{red}{+8} \color{blue}{-8} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{-8} \\\Leftrightarrow & 60x+27x& = & 4-8 \\\Leftrightarrow & \color{red}{87} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{87} & & \\ & V = \left\{ \frac{-4}{87} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & 4x+\frac{7}{10} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 4x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1050}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{280}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1050x \color{red}{-100} & = & \color{red}{280x} +49 \\\Leftrightarrow & -1050x \color{red}{-100} \color{blue}{+100} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{+100} \\\Leftrightarrow & -1050x-280x& = & 49+100 \\\Leftrightarrow & \color{red}{-1330} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-1330} & & \\\Leftrightarrow & x = \frac{-149}{1330} & & \\ & V = \left\{ \frac{-149}{1330} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{11})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{9}{11}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+45} & = & \color{red}{275x} +44 \\\Leftrightarrow & 660x \color{red}{+45} \color{blue}{-45} \color{blue}{-275x} & = & \color{red}{275x} +44 \color{blue}{-275x} \color{blue}{-45} \\\Leftrightarrow & 660x-275x& = & 44-45 \\\Leftrightarrow & \color{red}{385} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{385} & & \\ & V = \left\{ \frac{-1}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{2})& = & -8x+\frac{9}{8} \\\Leftrightarrow & 35x-\frac{35}{2}& = & -8x+\frac{9}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{280}{ \color{blue}{8} }x- \frac{140}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 280x \color{red}{-140} & = & \color{red}{-64x} +9 \\\Leftrightarrow & 280x \color{red}{-140} \color{blue}{+140} \color{blue}{+64x} & = & \color{red}{-64x} +9 \color{blue}{+64x} \color{blue}{+140} \\\Leftrightarrow & 280x+64x& = & 9+140 \\\Leftrightarrow & \color{red}{344} x& = & 149 \\\Leftrightarrow & x = \frac{149}{344} & & \\ & V = \left\{ \frac{149}{344} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{3})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x-\frac{28}{3}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{-28} & = & \color{red}{-24x} +8 \\\Leftrightarrow & -63x \color{red}{-28} \color{blue}{+28} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{+28} \\\Leftrightarrow & -63x+24x& = & 8+28 \\\Leftrightarrow & \color{red}{-39} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-39} & & \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -14x+\frac{14}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1078}{ \color{blue}{77} }x+ \frac{98}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1078x \color{red}{+98} & = & \color{red}{-385x} +110 \\\Leftrightarrow & -1078x \color{red}{+98} \color{blue}{-98} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-98} \\\Leftrightarrow & -1078x+385x& = & 110-98 \\\Leftrightarrow & \color{red}{-693} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-693} & & \\\Leftrightarrow & x = \frac{-4}{231} & & \\ & V = \left\{ \frac{-4}{231} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{20}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-220} & = & \color{red}{385x} +42 \\\Leftrightarrow & 924x \color{red}{-220} \color{blue}{+220} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+220} \\\Leftrightarrow & 924x-385x& = & 42+220 \\\Leftrightarrow & \color{red}{539} x& = & 262 \\\Leftrightarrow & x = \frac{262}{539} & & \\ & V = \left\{ \frac{262}{539} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{11})& = & 9x+\frac{7}{8} \\\Leftrightarrow & 14x-\frac{28}{11}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1232}{ \color{blue}{88} }x- \frac{224}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1232x \color{red}{-224} & = & \color{red}{792x} +77 \\\Leftrightarrow & 1232x \color{red}{-224} \color{blue}{+224} \color{blue}{-792x} & = & \color{red}{792x} +77 \color{blue}{-792x} \color{blue}{+224} \\\Leftrightarrow & 1232x-792x& = & 77+224 \\\Leftrightarrow & \color{red}{440} x& = & 301 \\\Leftrightarrow & x = \frac{301}{440} & & \\ & V = \left\{ \frac{301}{440} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{+16} & = & \color{red}{-30x} +9 \\\Leftrightarrow & 48x \color{red}{+16} \color{blue}{-16} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{-16} \\\Leftrightarrow & 48x+30x& = & 9-16 \\\Leftrightarrow & \color{red}{78} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{78} & & \\ & V = \left\{ \frac{-7}{78} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-8} & = & \color{red}{70x} +3 \\\Leftrightarrow & -60x \color{red}{-8} \color{blue}{+8} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{+8} \\\Leftrightarrow & -60x-70x& = & 3+8 \\\Leftrightarrow & \color{red}{-130} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-130} & & \\\Leftrightarrow & x = \frac{-11}{130} & & \\ & V = \left\{ \frac{-11}{130} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-160}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -160x \color{red}{-24} & = & \color{red}{70x} +45 \\\Leftrightarrow & -160x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & -160x-70x& = & 45+24 \\\Leftrightarrow & \color{red}{-230} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-230} & & \\\Leftrightarrow & x = \frac{-3}{10} & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)