Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-x+5)=2-(-7+x)\)
2. \(6(5x+7)=14+(15+x)\)
3. \(6(-6x-6)=8+(1+x)\)
4. \(6(4x+7)=-1-(-6+x)\)
5. \(6(4x+2)=1+(8+x)\)
6. \(5(x-1)=1-(2+x)\)
7. \(3(3x+5)=9+(-5+x)\)
8. \(4(-5x-4)=14+(7+x)\)
9. \(2(x-5)=-14-(6+x)\)
10. \(3(4x-6)=-3+(-6+x)\)
11. \(6(6x-1)=1-(4+x)\)
12. \(5(-6x+2)=6+(-2+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x+5)& = & 2 \color{red}{-} (-7+x) \\\Leftrightarrow & -3x+15& = &2+7-x \\\Leftrightarrow & -3x \color{red}{+15} & = &9 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -3x+x& = &9-15 \\\Leftrightarrow & -2x& = &-6 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-6}{ \color{red}{-2} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x+7)& = & 14 \color{red}{+} (15+x) \\\Leftrightarrow & 30x+42& = &14+15+x \\\Leftrightarrow & 30x \color{red}{+42} & = &29 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &29-42 \\\Leftrightarrow & 29x& = &-13 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-13}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-13}{29} & & \\ & V = \left\{ \frac{-13}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-6x-6)& = & 8 \color{red}{+} (1+x) \\\Leftrightarrow & -36x-36& = &8+1+x \\\Leftrightarrow & -36x \color{red}{-36} & = &9 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -36x-x& = &9+36 \\\Leftrightarrow & -37x& = &45 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{45}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-45}{37} & & \\ & V = \left\{ \frac{-45}{37} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x+7)& = & -1 \color{red}{-} (-6+x) \\\Leftrightarrow & 24x+42& = &-1+6-x \\\Leftrightarrow & 24x \color{red}{+42} & = &5 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &5-42 \\\Leftrightarrow & 25x& = &-37 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-37}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-37}{25} & & \\ & V = \left\{ \frac{-37}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x+2)& = & 1 \color{red}{+} (8+x) \\\Leftrightarrow & 24x+12& = &1+8+x \\\Leftrightarrow & 24x \color{red}{+12} & = &9 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &9-12 \\\Leftrightarrow & 23x& = &-3 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-3}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x-1)& = & 1 \color{red}{-} (2+x) \\\Leftrightarrow & 5x-5& = &1-2-x \\\Leftrightarrow & 5x \color{red}{-5} & = &-1 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 5x+x& = &-1+5 \\\Leftrightarrow & 6x& = &4 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{4}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+5)& = & 9 \color{red}{+} (-5+x) \\\Leftrightarrow & 9x+15& = &9-5+x \\\Leftrightarrow & 9x \color{red}{+15} & = &4 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 9x-x& = &4-15 \\\Leftrightarrow & 8x& = &-11 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-11}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-11}{8} & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-4)& = & 14 \color{red}{+} (7+x) \\\Leftrightarrow & -20x-16& = &14+7+x \\\Leftrightarrow & -20x \color{red}{-16} & = &21 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -20x-x& = &21+16 \\\Leftrightarrow & -21x& = &37 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{37}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-37}{21} & & \\ & V = \left\{ \frac{-37}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x-5)& = & -14 \color{red}{-} (6+x) \\\Leftrightarrow & 2x-10& = &-14-6-x \\\Leftrightarrow & 2x \color{red}{-10} & = &-20 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 2x+x& = &-20+10 \\\Leftrightarrow & 3x& = &-10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-6)& = & -3 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x-18& = &-3-6+x \\\Leftrightarrow & 12x \color{red}{-18} & = &-9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &-9+18 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x-1)& = & 1 \color{red}{-} (4+x) \\\Leftrightarrow & 36x-6& = &1-4-x \\\Leftrightarrow & 36x \color{red}{-6} & = &-3 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 36x+x& = &-3+6 \\\Leftrightarrow & 37x& = &3 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{3}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{3}{37} & & \\ & V = \left\{ \frac{3}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+2)& = & 6 \color{red}{+} (-2+x) \\\Leftrightarrow & -30x+10& = &6-2+x \\\Leftrightarrow & -30x \color{red}{+10} & = &4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -30x-x& = &4-10 \\\Leftrightarrow & -31x& = &-6 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-6}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)