Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & 2x+\frac{7}{5} \\\Leftrightarrow & 15x+\frac{9}{5}& = & 2x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{10}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+9} & = & \color{red}{10x} +7 \\\Leftrightarrow & 75x \color{red}{+9} \color{blue}{-9} \color{blue}{-10x} & = & \color{red}{10x} +7 \color{blue}{-10x} \color{blue}{-9} \\\Leftrightarrow & 75x-10x& = & 7-9 \\\Leftrightarrow & \color{red}{65} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{65} & & \\ & V = \left\{ \frac{-2}{65} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-60} & = & \color{red}{63x} +2 \\\Leftrightarrow & 180x \color{red}{-60} \color{blue}{+60} \color{blue}{-63x} & = & \color{red}{63x} +2 \color{blue}{-63x} \color{blue}{+60} \\\Leftrightarrow & 180x-63x& = & 2+60 \\\Leftrightarrow & \color{red}{117} x& = & 62 \\\Leftrightarrow & x = \frac{62}{117} & & \\ & V = \left\{ \frac{62}{117} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{2})& = & -2x+\frac{2}{7} \\\Leftrightarrow & 25x+\frac{15}{2}& = & -2x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{350}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{+105} & = & \color{red}{-28x} +4 \\\Leftrightarrow & 350x \color{red}{+105} \color{blue}{-105} \color{blue}{+28x} & = & \color{red}{-28x} +4 \color{blue}{+28x} \color{blue}{-105} \\\Leftrightarrow & 350x+28x& = & 4-105 \\\Leftrightarrow & \color{red}{378} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{378} & & \\ & V = \left\{ \frac{-101}{378} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-288}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -288x \color{red}{-32} & = & \color{red}{108x} +81 \\\Leftrightarrow & -288x \color{red}{-32} \color{blue}{+32} \color{blue}{-108x} & = & \color{red}{108x} +81 \color{blue}{-108x} \color{blue}{+32} \\\Leftrightarrow & -288x-108x& = & 81+32 \\\Leftrightarrow & \color{red}{-396} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-396} & & \\\Leftrightarrow & x = \frac{-113}{396} & & \\ & V = \left\{ \frac{-113}{396} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{7})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{18}{7}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{198}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+198} & = & \color{red}{-616x} +42 \\\Leftrightarrow & -1386x \color{red}{+198} \color{blue}{-198} \color{blue}{+616x} & = & \color{red}{-616x} +42 \color{blue}{+616x} \color{blue}{-198} \\\Leftrightarrow & -1386x+616x& = & 42-198 \\\Leftrightarrow & \color{red}{-770} x& = & -156 \\\Leftrightarrow & x = \frac{-156}{-770} & & \\\Leftrightarrow & x = \frac{78}{385} & & \\ & V = \left\{ \frac{78}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{4})& = & 8x+\frac{8}{3} \\\Leftrightarrow & 9x+\frac{15}{4}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{108}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 108x \color{red}{+45} & = & \color{red}{96x} +32 \\\Leftrightarrow & 108x \color{red}{+45} \color{blue}{-45} \color{blue}{-96x} & = & \color{red}{96x} +32 \color{blue}{-96x} \color{blue}{-45} \\\Leftrightarrow & 108x-96x& = & 32-45 \\\Leftrightarrow & \color{red}{12} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{12} & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & -9x+\frac{9}{5} \\\Leftrightarrow & -8x-\frac{12}{11}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-60} & = & \color{red}{-495x} +99 \\\Leftrightarrow & -440x \color{red}{-60} \color{blue}{+60} \color{blue}{+495x} & = & \color{red}{-495x} +99 \color{blue}{+495x} \color{blue}{+60} \\\Leftrightarrow & -440x+495x& = & 99+60 \\\Leftrightarrow & \color{red}{55} x& = & 159 \\\Leftrightarrow & x = \frac{159}{55} & & \\ & V = \left\{ \frac{159}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -9x-\frac{6}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{-54} & = & \color{red}{225x} +10 \\\Leftrightarrow & -405x \color{red}{-54} \color{blue}{+54} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{+54} \\\Leftrightarrow & -405x-225x& = & 10+54 \\\Leftrightarrow & \color{red}{-630} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-630} & & \\\Leftrightarrow & x = \frac{-32}{315} & & \\ & V = \left\{ \frac{-32}{315} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 7x+\frac{3}{5} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{+12} & = & \color{red}{35x} +3 \\\Leftrightarrow & 100x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 100x-35x& = & 3-12 \\\Leftrightarrow & \color{red}{65} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{65} & & \\ & V = \left\{ \frac{-9}{65} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 135x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 135x+75x& = & 10+36 \\\Leftrightarrow & \color{red}{210} x& = & 46 \\\Leftrightarrow & x = \frac{46}{210} & & \\\Leftrightarrow & x = \frac{23}{105} & & \\ & V = \left\{ \frac{23}{105} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{15}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-165} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -770x \color{red}{-165} \color{blue}{+165} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+165} \\\Leftrightarrow & -770x+539x& = & 42+165 \\\Leftrightarrow & \color{red}{-231} x& = & 207 \\\Leftrightarrow & x = \frac{207}{-231} & & \\\Leftrightarrow & x = \frac{-69}{77} & & \\ & V = \left\{ \frac{-69}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 24x+\frac{24}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1512}{ \color{blue}{63} }x+ \frac{216}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1512x \color{red}{+216} & = & \color{red}{315x} +70 \\\Leftrightarrow & 1512x \color{red}{+216} \color{blue}{-216} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{-216} \\\Leftrightarrow & 1512x-315x& = & 70-216 \\\Leftrightarrow & \color{red}{1197} x& = & -146 \\\Leftrightarrow & x = \frac{-146}{1197} & & \\ & V = \left\{ \frac{-146}{1197} \right\} & \\\end{align}\)