Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & -4x+\frac{9}{10} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -4x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1050}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-280}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1050x \color{red}{-60} & = & \color{red}{-280x} +63 \\\Leftrightarrow & -1050x \color{red}{-60} \color{blue}{+60} \color{blue}{+280x} & = & \color{red}{-280x} +63 \color{blue}{+280x} \color{blue}{+60} \\\Leftrightarrow & -1050x+280x& = & 63+60 \\\Leftrightarrow & \color{red}{-770} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-770} & & \\\Leftrightarrow & x = \frac{-123}{770} & & \\ & V = \left\{ \frac{-123}{770} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{3})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -16x+\frac{8}{3}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+40} & = & \color{red}{-105x} +6 \\\Leftrightarrow & -240x \color{red}{+40} \color{blue}{-40} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{-40} \\\Leftrightarrow & -240x+105x& = & 6-40 \\\Leftrightarrow & \color{red}{-135} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-135} & & \\\Leftrightarrow & x = \frac{34}{135} & & \\ & V = \left\{ \frac{34}{135} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{9})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 20x-\frac{25}{9}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{275}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-275} & = & \color{red}{693x} +45 \\\Leftrightarrow & 1980x \color{red}{-275} \color{blue}{+275} \color{blue}{-693x} & = & \color{red}{693x} +45 \color{blue}{-693x} \color{blue}{+275} \\\Leftrightarrow & 1980x-693x& = & 45+275 \\\Leftrightarrow & \color{red}{1287} x& = & 320 \\\Leftrightarrow & x = \frac{320}{1287} & & \\ & V = \left\{ \frac{320}{1287} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{-4} & = & \color{red}{25x} +7 \\\Leftrightarrow & 40x \color{red}{-4} \color{blue}{+4} \color{blue}{-25x} & = & \color{red}{25x} +7 \color{blue}{-25x} \color{blue}{+4} \\\Leftrightarrow & 40x-25x& = & 7+4 \\\Leftrightarrow & \color{red}{15} x& = & 11 \\\Leftrightarrow & x = \frac{11}{15} & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+66} & = & \color{red}{-275x} +10 \\\Leftrightarrow & 330x \color{red}{+66} \color{blue}{-66} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{-66} \\\Leftrightarrow & 330x+275x& = & 10-66 \\\Leftrightarrow & \color{red}{605} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{605} & & \\ & V = \left\{ \frac{-56}{605} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{9}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{50x} +15 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{+18} \\\Leftrightarrow & 120x-50x& = & 15+18 \\\Leftrightarrow & \color{red}{70} x& = & 33 \\\Leftrightarrow & x = \frac{33}{70} & & \\ & V = \left\{ \frac{33}{70} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{+6} & = & \color{red}{-63x} +3 \\\Leftrightarrow & -28x \color{red}{+6} \color{blue}{-6} \color{blue}{+63x} & = & \color{red}{-63x} +3 \color{blue}{+63x} \color{blue}{-6} \\\Leftrightarrow & -28x+63x& = & 3-6 \\\Leftrightarrow & \color{red}{35} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{35} & & \\ & V = \left\{ \frac{-3}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{-40} & = & \color{red}{-315x} +63 \\\Leftrightarrow & -720x \color{red}{-40} \color{blue}{+40} \color{blue}{+315x} & = & \color{red}{-315x} +63 \color{blue}{+315x} \color{blue}{+40} \\\Leftrightarrow & -720x+315x& = & 63+40 \\\Leftrightarrow & \color{red}{-405} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-405} & & \\\Leftrightarrow & x = \frac{-103}{405} & & \\ & V = \left\{ \frac{-103}{405} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 16x-\frac{16}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x- \frac{176}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{-176} & = & \color{red}{-231x} +18 \\\Leftrightarrow & 528x \color{red}{-176} \color{blue}{+176} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{+176} \\\Leftrightarrow & 528x+231x& = & 18+176 \\\Leftrightarrow & \color{red}{759} x& = & 194 \\\Leftrightarrow & x = \frac{194}{759} & & \\ & V = \left\{ \frac{194}{759} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+40} & = & \color{red}{-196x} +21 \\\Leftrightarrow & -168x \color{red}{+40} \color{blue}{-40} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{-40} \\\Leftrightarrow & -168x+196x& = & 21-40 \\\Leftrightarrow & \color{red}{28} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{28} & & \\ & V = \left\{ \frac{-19}{28} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -4x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+66} & = & \color{red}{-308x} +14 \\\Leftrightarrow & -1155x \color{red}{+66} \color{blue}{-66} \color{blue}{+308x} & = & \color{red}{-308x} +14 \color{blue}{+308x} \color{blue}{-66} \\\Leftrightarrow & -1155x+308x& = & 14-66 \\\Leftrightarrow & \color{red}{-847} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-847} & & \\\Leftrightarrow & x = \frac{52}{847} & & \\ & V = \left\{ \frac{52}{847} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{-90} & = & \color{red}{147x} +56 \\\Leftrightarrow & 504x \color{red}{-90} \color{blue}{+90} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+90} \\\Leftrightarrow & 504x-147x& = & 56+90 \\\Leftrightarrow & \color{red}{357} x& = & 146 \\\Leftrightarrow & x = \frac{146}{357} & & \\ & V = \left\{ \frac{146}{357} \right\} & \\\end{align}\)