Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x-5)& = & 1 \color{red}{-} (-1+x) \\\Leftrightarrow & -24x-20& = &1+1-x \\\Leftrightarrow & -24x \color{red}{-20} & = &2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -24x+x& = &2+20 \\\Leftrightarrow & -23x& = &22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-6)& = & 12 \color{red}{+} (-7-2x) \\\Leftrightarrow & 15x-18& = &12-7-2x \\\Leftrightarrow & 15x \color{red}{-18} & = &5 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 15x+2x& = &5+18 \\\Leftrightarrow & 17x& = &23 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{23}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{23}{17} & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x-1)& = & 7 \color{red}{-} (-6-5x) \\\Leftrightarrow & -18x-6& = &7+6+5x \\\Leftrightarrow & -18x \color{red}{-6} & = &13 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -18x-5x& = &13+6 \\\Leftrightarrow & -23x& = &19 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{19}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-19}{23} & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x-4)& = & 9 \color{red}{+} (-4+x) \\\Leftrightarrow & 10x-8& = &9-4+x \\\Leftrightarrow & 10x \color{red}{-8} & = &5 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 10x-x& = &5+8 \\\Leftrightarrow & 9x& = &13 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{13}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{13}{9} & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x+4)& = & 12 \color{red}{-} (-4-2x) \\\Leftrightarrow & 15x+20& = &12+4+2x \\\Leftrightarrow & 15x \color{red}{+20} & = &16 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & 15x-2x& = &16-20 \\\Leftrightarrow & 13x& = &-4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x+1)& = & -11 \color{red}{+} (-5+x) \\\Leftrightarrow & -4x+2& = &-11-5+x \\\Leftrightarrow & -4x \color{red}{+2} & = &-16 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -4x-x& = &-16-2 \\\Leftrightarrow & -5x& = &-18 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-18}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-6)& = & 5 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x-30& = &5+12-x \\\Leftrightarrow & -30x \color{red}{-30} & = &17 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -30x+x& = &17+30 \\\Leftrightarrow & -29x& = &47 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{47}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-47}{29} & & \\ & V = \left\{ \frac{-47}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x-2)& = & 1 \color{red}{+} (-2+x) \\\Leftrightarrow & -2x-4& = &1-2+x \\\Leftrightarrow & -2x \color{red}{-4} & = &-1 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -2x-x& = &-1+4 \\\Leftrightarrow & -3x& = &3 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{3}{ \color{red}{-3} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x+5)& = & 4 \color{red}{-} (4+x) \\\Leftrightarrow & 6x+15& = &4-4-x \\\Leftrightarrow & 6x \color{red}{+15} & = &0 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 6x+x& = &0-15 \\\Leftrightarrow & 7x& = &-15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+7)& = & 9 \color{red}{+} (-9+x) \\\Leftrightarrow & 15x+21& = &9-9+x \\\Leftrightarrow & 15x \color{red}{+21} & = &0 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 15x-x& = &0-21 \\\Leftrightarrow & 14x& = &-21 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-21}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x-1)& = & -8 \color{red}{+} (3-5x) \\\Leftrightarrow & 6x-6& = &-8+3-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &-5+6 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x-3)& = & 15 \color{red}{+} (6+x) \\\Leftrightarrow & -4x-12& = &15+6+x \\\Leftrightarrow & -4x \color{red}{-12} & = &21 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -4x-x& = &21+12 \\\Leftrightarrow & -5x& = &33 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{33}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-33}{5} & & \\ & V = \left\{ \frac{-33}{5} \right\} & \\\end{align}\)