Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(5(-3x-4)=9+(7-2x)\)
2. \(6(-4x+3)=-13+(-2+x)\)
3. \(4(x-2)=14+(-5+3x)\)
4. \(2(-6x+5)=6-(-8+x)\)
5. \(5(5x-5)=1-(1+x)\)
6. \(5(-3x+2)=-10+(8-2x)\)
7. \(4(5x-4)=14+(3+x)\)
8. \(5(4x+7)=-2+(9+x)\)
9. \(4(-5x-4)=-3-(4+x)\)
10. \(5(2x-1)=-14-(-10+x)\)
11. \(6(2x+5)=6+(-14+x)\)
12. \(5(-5x-5)=-15+(14+2x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x-4)& = & 9 \color{red}{+} (7-2x) \\\Leftrightarrow & -15x-20& = &9+7-2x \\\Leftrightarrow & -15x \color{red}{-20} & = &16 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & -15x+2x& = &16+20 \\\Leftrightarrow & -13x& = &36 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{36}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+3)& = & -13 \color{red}{+} (-2+x) \\\Leftrightarrow & -24x+18& = &-13-2+x \\\Leftrightarrow & -24x \color{red}{+18} & = &-15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -24x-x& = &-15-18 \\\Leftrightarrow & -25x& = &-33 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-33}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{33}{25} & & \\ & V = \left\{ \frac{33}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-2)& = & 14 \color{red}{+} (-5+3x) \\\Leftrightarrow & 4x-8& = &14-5+3x \\\Leftrightarrow & 4x \color{red}{-8} & = &9 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 4x-3x& = &9+8 \\\Leftrightarrow & x& = &17 \\ & V = \left\{ 17 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x+5)& = & 6 \color{red}{-} (-8+x) \\\Leftrightarrow & -12x+10& = &6+8-x \\\Leftrightarrow & -12x \color{red}{+10} & = &14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &14-10 \\\Leftrightarrow & -11x& = &4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x-5)& = & 1 \color{red}{-} (1+x) \\\Leftrightarrow & 25x-25& = &1-1-x \\\Leftrightarrow & 25x \color{red}{-25} & = &0 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 25x+x& = &0+25 \\\Leftrightarrow & 26x& = &25 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{25}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{25}{26} & & \\ & V = \left\{ \frac{25}{26} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+2)& = & -10 \color{red}{+} (8-2x) \\\Leftrightarrow & -15x+10& = &-10+8-2x \\\Leftrightarrow & -15x \color{red}{+10} & = &-2 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & -15x+2x& = &-2-10 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x-4)& = & 14 \color{red}{+} (3+x) \\\Leftrightarrow & 20x-16& = &14+3+x \\\Leftrightarrow & 20x \color{red}{-16} & = &17 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 20x-x& = &17+16 \\\Leftrightarrow & 19x& = &33 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{33}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{33}{19} & & \\ & V = \left\{ \frac{33}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x+7)& = & -2 \color{red}{+} (9+x) \\\Leftrightarrow & 20x+35& = &-2+9+x \\\Leftrightarrow & 20x \color{red}{+35} & = &7 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 20x-x& = &7-35 \\\Leftrightarrow & 19x& = &-28 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-28}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-28}{19} & & \\ & V = \left\{ \frac{-28}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x-4)& = & -3 \color{red}{-} (4+x) \\\Leftrightarrow & -20x-16& = &-3-4-x \\\Leftrightarrow & -20x \color{red}{-16} & = &-7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &-7+16 \\\Leftrightarrow & -19x& = &9 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{9}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-9}{19} & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-1)& = & -14 \color{red}{-} (-10+x) \\\Leftrightarrow & 10x-5& = &-14+10-x \\\Leftrightarrow & 10x \color{red}{-5} & = &-4 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 10x+x& = &-4+5 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x+5)& = & 6 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+30& = &6-14+x \\\Leftrightarrow & 12x \color{red}{+30} & = &-8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 12x-x& = &-8-30 \\\Leftrightarrow & 11x& = &-38 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-38}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-38}{11} & & \\ & V = \left\{ \frac{-38}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x-5)& = & -15 \color{red}{+} (14+2x) \\\Leftrightarrow & -25x-25& = &-15+14+2x \\\Leftrightarrow & -25x \color{red}{-25} & = &-1 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & -25x-2x& = &-1+25 \\\Leftrightarrow & -27x& = &24 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{24}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)