Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x+1)& = & -14 \color{red}{+} (7+3x) \\\Leftrightarrow & -2x+2& = &-14+7+3x \\\Leftrightarrow & -2x \color{red}{+2} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -2x-3x& = &-7-2 \\\Leftrightarrow & -5x& = &-9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x+2)& = & 14 \color{red}{+} (-6+x) \\\Leftrightarrow & -24x+8& = &14-6+x \\\Leftrightarrow & -24x \color{red}{+8} & = &8 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -24x-x& = &8-8 \\\Leftrightarrow & -25x& = &0 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{0}{ \color{red}{-25} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-4)& = & 9 \color{red}{-} (-2+x) \\\Leftrightarrow & 24x-24& = &9+2-x \\\Leftrightarrow & 24x \color{red}{-24} & = &11 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &11+24 \\\Leftrightarrow & 25x& = &35 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{35}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x+6)& = & -15 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x+36& = &-15-9+x \\\Leftrightarrow & 24x \color{red}{+36} & = &-24 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 24x-x& = &-24-36 \\\Leftrightarrow & 23x& = &-60 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-60}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-60}{23} & & \\ & V = \left\{ \frac{-60}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x-1)& = & -8 \color{red}{+} (-7+x) \\\Leftrightarrow & 15x-3& = &-8-7+x \\\Leftrightarrow & 15x \color{red}{-3} & = &-15 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 15x-x& = &-15+3 \\\Leftrightarrow & 14x& = &-12 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-12}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-5x+4)& = & 8 \color{red}{+} (7+3x) \\\Leftrightarrow & -20x+16& = &8+7+3x \\\Leftrightarrow & -20x \color{red}{+16} & = &15 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & -20x-3x& = &15-16 \\\Leftrightarrow & -23x& = &-1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x+2)& = & -12 \color{red}{+} (14+3x) \\\Leftrightarrow & -8x+8& = &-12+14+3x \\\Leftrightarrow & -8x \color{red}{+8} & = &2 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -8x-3x& = &2-8 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x-5)& = & 11 \color{red}{+} (-15+x) \\\Leftrightarrow & 9x-15& = &11-15+x \\\Leftrightarrow & 9x \color{red}{-15} & = &-4 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 9x-x& = &-4+15 \\\Leftrightarrow & 8x& = &11 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{11}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{11}{8} & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x-1)& = & -14 \color{red}{-} (-12+x) \\\Leftrightarrow & 15x-5& = &-14+12-x \\\Leftrightarrow & 15x \color{red}{-5} & = &-2 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 15x+x& = &-2+5 \\\Leftrightarrow & 16x& = &3 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{3}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{3}{16} & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x+7)& = & -8 \color{red}{+} (-4-3x) \\\Leftrightarrow & 10x+35& = &-8-4-3x \\\Leftrightarrow & 10x \color{red}{+35} & = &-12 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & 10x+3x& = &-12-35 \\\Leftrightarrow & 13x& = &-47 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-47}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-47}{13} & & \\ & V = \left\{ \frac{-47}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x+1)& = & -12 \color{red}{+} (-14+2x) \\\Leftrightarrow & 25x+5& = &-12-14+2x \\\Leftrightarrow & 25x \color{red}{+5} & = &-26 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &-26 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & 25x-2x& = &-26-5 \\\Leftrightarrow & 23x& = &-31 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-31}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-31}{23} & & \\ & V = \left\{ \frac{-31}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-2)& = & -9 \color{red}{+} (6-5x) \\\Leftrightarrow & -16x-8& = &-9+6-5x \\\Leftrightarrow & -16x \color{red}{-8} & = &-3 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & -16x+5x& = &-3+8 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)