Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(-5x+3)=12-(8+x)\)
2. \(2(-2x-2)=-2-(13+x)\)
3. \(3(x+7)=2-(-14-5x)\)
4. \(5(-x-4)=12+(4+4x)\)
5. \(6(2x+1)=-2+(3+x)\)
6. \(6(3x+6)=-13-(12+x)\)
7. \(3(-x+1)=11-(-1+2x)\)
8. \(5(x+2)=-13+(-4+x)\)
9. \(5(-4x-3)=1-(-1+3x)\)
10. \(5(-3x+3)=7+(11-2x)\)
11. \(5(-6x-3)=-10-(-1+x)\)
12. \(5(-3x-7)=2-(-13-2x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+3)& = & 12 \color{red}{-} (8+x) \\\Leftrightarrow & -30x+18& = &12-8-x \\\Leftrightarrow & -30x \color{red}{+18} & = &4 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -30x+x& = &4-18 \\\Leftrightarrow & -29x& = &-14 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-14}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{14}{29} & & \\ & V = \left\{ \frac{14}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x-2)& = & -2 \color{red}{-} (13+x) \\\Leftrightarrow & -4x-4& = &-2-13-x \\\Leftrightarrow & -4x \color{red}{-4} & = &-15 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -4x+x& = &-15+4 \\\Leftrightarrow & -3x& = &-11 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-11}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x+7)& = & 2 \color{red}{-} (-14-5x) \\\Leftrightarrow & 3x+21& = &2+14+5x \\\Leftrightarrow & 3x \color{red}{+21} & = &16 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & 3x-5x& = &16-21 \\\Leftrightarrow & -2x& = &-5 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-5}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{5}{2} & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-x-4)& = & 12 \color{red}{+} (4+4x) \\\Leftrightarrow & -5x-20& = &12+4+4x \\\Leftrightarrow & -5x \color{red}{-20} & = &16 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -5x-4x& = &16+20 \\\Leftrightarrow & -9x& = &36 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{36}{ \color{red}{-9} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x+1)& = & -2 \color{red}{+} (3+x) \\\Leftrightarrow & 12x+6& = &-2+3+x \\\Leftrightarrow & 12x \color{red}{+6} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &1-6 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x+6)& = & -13 \color{red}{-} (12+x) \\\Leftrightarrow & 18x+36& = &-13-12-x \\\Leftrightarrow & 18x \color{red}{+36} & = &-25 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 18x+x& = &-25-36 \\\Leftrightarrow & 19x& = &-61 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-61}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-61}{19} & & \\ & V = \left\{ \frac{-61}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+1)& = & 11 \color{red}{-} (-1+2x) \\\Leftrightarrow & -3x+3& = &11+1-2x \\\Leftrightarrow & -3x \color{red}{+3} & = &12 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & -3x+2x& = &12-3 \\\Leftrightarrow & -x& = &9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{9}{ \color{red}{-1} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x+2)& = & -13 \color{red}{+} (-4+x) \\\Leftrightarrow & 5x+10& = &-13-4+x \\\Leftrightarrow & 5x \color{red}{+10} & = &-17 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 5x-x& = &-17-10 \\\Leftrightarrow & 4x& = &-27 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-27}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-27}{4} & & \\ & V = \left\{ \frac{-27}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x-3)& = & 1 \color{red}{-} (-1+3x) \\\Leftrightarrow & -20x-15& = &1+1-3x \\\Leftrightarrow & -20x \color{red}{-15} & = &2 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & -20x+3x& = &2+15 \\\Leftrightarrow & -17x& = &17 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{17}{ \color{red}{-17} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x+3)& = & 7 \color{red}{+} (11-2x) \\\Leftrightarrow & -15x+15& = &7+11-2x \\\Leftrightarrow & -15x \color{red}{+15} & = &18 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & -15x+2x& = &18-15 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x-3)& = & -10 \color{red}{-} (-1+x) \\\Leftrightarrow & -30x-15& = &-10+1-x \\\Leftrightarrow & -30x \color{red}{-15} & = &-9 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -30x+x& = &-9+15 \\\Leftrightarrow & -29x& = &6 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{6}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-6}{29} & & \\ & V = \left\{ \frac{-6}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x-7)& = & 2 \color{red}{-} (-13-2x) \\\Leftrightarrow & -15x-35& = &2+13+2x \\\Leftrightarrow & -15x \color{red}{-35} & = &15 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & -15x-2x& = &15+35 \\\Leftrightarrow & -17x& = &50 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{50}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-50}{17} & & \\ & V = \left\{ \frac{-50}{17} \right\} & \\\end{align}\)