Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{2})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 9x-\frac{15}{2}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{18}{ \color{blue}{2} }x- \frac{15}{ \color{blue}{2} })& = & (\frac{14}{ \color{blue}{2} }x+ \frac{7}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 18x \color{red}{-15} & = & \color{red}{14x} +7 \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{-14x} & = & \color{red}{14x} +7 \color{blue}{-14x} \color{blue}{+15} \\\Leftrightarrow & 18x-14x& = & 7+15 \\\Leftrightarrow & \color{red}{4} x& = & 22 \\\Leftrightarrow & x = \frac{22}{4} & & \\\Leftrightarrow & x = \frac{11}{2} & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{9})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{20}{9}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+20} & = & \color{red}{-27x} +24 \\\Leftrightarrow & 180x \color{red}{+20} \color{blue}{-20} \color{blue}{+27x} & = & \color{red}{-27x} +24 \color{blue}{+27x} \color{blue}{-20} \\\Leftrightarrow & 180x+27x& = & 24-20 \\\Leftrightarrow & \color{red}{207} x& = & 4 \\\Leftrightarrow & x = \frac{4}{207} & & \\ & V = \left\{ \frac{4}{207} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{8}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+8} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -132x \color{red}{+8} \color{blue}{-8} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-8} \\\Leftrightarrow & -132x+55x& = & 6-8 \\\Leftrightarrow & \color{red}{-77} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-77} & & \\\Leftrightarrow & x = \frac{2}{77} & & \\ & V = \left\{ \frac{2}{77} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{8})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -6x-\frac{15}{8}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-48}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -48x \color{red}{-15} & = & \color{red}{56x} +36 \\\Leftrightarrow & -48x \color{red}{-15} \color{blue}{+15} \color{blue}{-56x} & = & \color{red}{56x} +36 \color{blue}{-56x} \color{blue}{+15} \\\Leftrightarrow & -48x-56x& = & 36+15 \\\Leftrightarrow & \color{red}{-104} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-104} & & \\\Leftrightarrow & x = \frac{-51}{104} & & \\ & V = \left\{ \frac{-51}{104} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+12} & = & \color{red}{-25x} +3 \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +3 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 30x+25x& = & 3-12 \\\Leftrightarrow & \color{red}{55} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{55} & & \\ & V = \left\{ \frac{-9}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+90} & = & \color{red}{275x} +66 \\\Leftrightarrow & 990x \color{red}{+90} \color{blue}{-90} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{-90} \\\Leftrightarrow & 990x-275x& = & 66-90 \\\Leftrightarrow & \color{red}{715} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{715} & & \\ & V = \left\{ \frac{-24}{715} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{5})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+132} & = & \color{red}{165x} +20 \\\Leftrightarrow & 880x \color{red}{+132} \color{blue}{-132} \color{blue}{-165x} & = & \color{red}{165x} +20 \color{blue}{-165x} \color{blue}{-132} \\\Leftrightarrow & 880x-165x& = & 20-132 \\\Leftrightarrow & \color{red}{715} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{715} & & \\ & V = \left\{ \frac{-112}{715} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & -8x+\frac{8}{5} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-50} & = & \color{red}{-280x} +56 \\\Leftrightarrow & 525x \color{red}{-50} \color{blue}{+50} \color{blue}{+280x} & = & \color{red}{-280x} +56 \color{blue}{+280x} \color{blue}{+50} \\\Leftrightarrow & 525x+280x& = & 56+50 \\\Leftrightarrow & \color{red}{805} x& = & 106 \\\Leftrightarrow & x = \frac{106}{805} & & \\ & V = \left\{ \frac{106}{805} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{-147x} +49 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +49 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -126x+147x& = & 49+18 \\\Leftrightarrow & \color{red}{21} x& = & 67 \\\Leftrightarrow & x = \frac{67}{21} & & \\ & V = \left\{ \frac{67}{21} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{4})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -6x-\frac{9}{4}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x- \frac{99}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{-99} & = & \color{red}{308x} +32 \\\Leftrightarrow & -264x \color{red}{-99} \color{blue}{+99} \color{blue}{-308x} & = & \color{red}{308x} +32 \color{blue}{-308x} \color{blue}{+99} \\\Leftrightarrow & -264x-308x& = & 32+99 \\\Leftrightarrow & \color{red}{-572} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-572} & & \\\Leftrightarrow & x = \frac{-131}{572} & & \\ & V = \left\{ \frac{-131}{572} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -6x-\frac{10}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-90} & = & \color{red}{693x} +110 \\\Leftrightarrow & -594x \color{red}{-90} \color{blue}{+90} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{+90} \\\Leftrightarrow & -594x-693x& = & 110+90 \\\Leftrightarrow & \color{red}{-1287} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-1287} & & \\\Leftrightarrow & x = \frac{-200}{1287} & & \\ & V = \left\{ \frac{-200}{1287} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-756}{ \color{blue}{84} }x- \frac{72}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -756x \color{red}{-72} & = & \color{red}{420x} +35 \\\Leftrightarrow & -756x \color{red}{-72} \color{blue}{+72} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{+72} \\\Leftrightarrow & -756x-420x& = & 35+72 \\\Leftrightarrow & \color{red}{-1176} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-1176} & & \\\Leftrightarrow & x = \frac{-107}{1176} & & \\ & V = \left\{ \frac{-107}{1176} \right\} & \\\end{align}\)