Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{7})& = & -4x+\frac{4}{7} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{+6} & = & \color{red}{-28x} +4 \\\Leftrightarrow & 63x \color{red}{+6} \color{blue}{-6} \color{blue}{+28x} & = & \color{red}{-28x} +4 \color{blue}{+28x} \color{blue}{-6} \\\Leftrightarrow & 63x+28x& = & 4-6 \\\Leftrightarrow & \color{red}{91} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{91} & & \\ & V = \left\{ \frac{-2}{91} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{2})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -14x-\frac{21}{2}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-252}{ \color{blue}{18} }x- \frac{189}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -252x \color{red}{-189} & = & \color{red}{-54x} +20 \\\Leftrightarrow & -252x \color{red}{-189} \color{blue}{+189} \color{blue}{+54x} & = & \color{red}{-54x} +20 \color{blue}{+54x} \color{blue}{+189} \\\Leftrightarrow & -252x+54x& = & 20+189 \\\Leftrightarrow & \color{red}{-198} x& = & 209 \\\Leftrightarrow & x = \frac{209}{-198} & & \\\Leftrightarrow & x = \frac{-19}{18} & & \\ & V = \left\{ \frac{-19}{18} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{3})& = & -3x+\frac{2}{9} \\\Leftrightarrow & -14x+\frac{28}{3}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x+ \frac{84}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{+84} & = & \color{red}{-27x} +2 \\\Leftrightarrow & -126x \color{red}{+84} \color{blue}{-84} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{-84} \\\Leftrightarrow & -126x+27x& = & 2-84 \\\Leftrightarrow & \color{red}{-99} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-99} & & \\\Leftrightarrow & x = \frac{82}{99} & & \\ & V = \left\{ \frac{82}{99} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{3})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 10x-\frac{8}{3}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-24} & = & \color{red}{-63x} +8 \\\Leftrightarrow & 90x \color{red}{-24} \color{blue}{+24} \color{blue}{+63x} & = & \color{red}{-63x} +8 \color{blue}{+63x} \color{blue}{+24} \\\Leftrightarrow & 90x+63x& = & 8+24 \\\Leftrightarrow & \color{red}{153} x& = & 32 \\\Leftrightarrow & x = \frac{32}{153} & & \\ & V = \left\{ \frac{32}{153} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{5})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -4x+\frac{6}{5}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{+66} & = & \color{red}{-275x} +45 \\\Leftrightarrow & -220x \color{red}{+66} \color{blue}{-66} \color{blue}{+275x} & = & \color{red}{-275x} +45 \color{blue}{+275x} \color{blue}{-66} \\\Leftrightarrow & -220x+275x& = & 45-66 \\\Leftrightarrow & \color{red}{55} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{55} & & \\ & V = \left\{ \frac{-21}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 4x+\frac{4}{7} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 4x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+6} & = & \color{red}{28x} +4 \\\Leftrightarrow & 105x \color{red}{+6} \color{blue}{-6} \color{blue}{-28x} & = & \color{red}{28x} +4 \color{blue}{-28x} \color{blue}{-6} \\\Leftrightarrow & 105x-28x& = & 4-6 \\\Leftrightarrow & \color{red}{77} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{77} & & \\ & V = \left\{ \frac{-2}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x- \frac{40}{ \color{blue}{90} })& = & (\frac{-450}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{-40} & = & \color{red}{-450x} +81 \\\Leftrightarrow & 540x \color{red}{-40} \color{blue}{+40} \color{blue}{+450x} & = & \color{red}{-450x} +81 \color{blue}{+450x} \color{blue}{+40} \\\Leftrightarrow & 540x+450x& = & 81+40 \\\Leftrightarrow & \color{red}{990} x& = & 121 \\\Leftrightarrow & x = \frac{121}{990} & & \\\Leftrightarrow & x = \frac{11}{90} & & \\ & V = \left\{ \frac{11}{90} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{30}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-150} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1650x \color{red}{-150} \color{blue}{+150} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+150} \\\Leftrightarrow & -1650x+385x& = & 66+150 \\\Leftrightarrow & \color{red}{-1265} x& = & 216 \\\Leftrightarrow & x = \frac{216}{-1265} & & \\\Leftrightarrow & x = \frac{-216}{1265} & & \\ & V = \left\{ \frac{-216}{1265} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-84} & = & \color{red}{315x} +40 \\\Leftrightarrow & 560x \color{red}{-84} \color{blue}{+84} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+84} \\\Leftrightarrow & 560x-315x& = & 40+84 \\\Leftrightarrow & \color{red}{245} x& = & 124 \\\Leftrightarrow & x = \frac{124}{245} & & \\ & V = \left\{ \frac{124}{245} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{10}{7}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+30} & = & \color{red}{-189x} +14 \\\Leftrightarrow & -84x \color{red}{+30} \color{blue}{-30} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{-30} \\\Leftrightarrow & -84x+189x& = & 14-30 \\\Leftrightarrow & \color{red}{105} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{105} & & \\ & V = \left\{ \frac{-16}{105} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+36} & = & \color{red}{-135x} +40 \\\Leftrightarrow & -300x \color{red}{+36} \color{blue}{-36} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{-36} \\\Leftrightarrow & -300x+135x& = & 40-36 \\\Leftrightarrow & \color{red}{-165} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-165} & & \\\Leftrightarrow & x = \frac{-4}{165} & & \\ & V = \left\{ \frac{-4}{165} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{4})& = & -4x+\frac{10}{9} \\\Leftrightarrow & -15x+\frac{9}{4}& = & -4x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-540}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} })& = & (\frac{-144}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -540x \color{red}{+81} & = & \color{red}{-144x} +40 \\\Leftrightarrow & -540x \color{red}{+81} \color{blue}{-81} \color{blue}{+144x} & = & \color{red}{-144x} +40 \color{blue}{+144x} \color{blue}{-81} \\\Leftrightarrow & -540x+144x& = & 40-81 \\\Leftrightarrow & \color{red}{-396} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-396} & & \\\Leftrightarrow & x = \frac{41}{396} & & \\ & V = \left\{ \frac{41}{396} \right\} & \\\end{align}\)