Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x+6)& = & -5 \color{red}{+} (-2+x) \\\Leftrightarrow & -2x+12& = &-5-2+x \\\Leftrightarrow & -2x \color{red}{+12} & = &-7 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -2x-x& = &-7-12 \\\Leftrightarrow & -3x& = &-19 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-19}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{19}{3} & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x+7)& = & -8 \color{red}{+} (15+x) \\\Leftrightarrow & 6x+42& = &-8+15+x \\\Leftrightarrow & 6x \color{red}{+42} & = &7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 6x-x& = &7-42 \\\Leftrightarrow & 5x& = &-35 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-35}{ \color{red}{5} } \\\Leftrightarrow & x = -7 & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x-1)& = & -2 \color{red}{+} (8+3x) \\\Leftrightarrow & -10x-2& = &-2+8+3x \\\Leftrightarrow & -10x \color{red}{-2} & = &6 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & -10x-3x& = &6+2 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x+1)& = & -5 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+4& = &-5-13-x \\\Leftrightarrow & 12x \color{red}{+4} & = &-18 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &-18-4 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x+7)& = & -5 \color{red}{+} (-11+x) \\\Leftrightarrow & 20x+35& = &-5-11+x \\\Leftrightarrow & 20x \color{red}{+35} & = &-16 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 20x-x& = &-16-35 \\\Leftrightarrow & 19x& = &-51 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-51}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-51}{19} & & \\ & V = \left\{ \frac{-51}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x-2)& = & -7 \color{red}{+} (14+3x) \\\Leftrightarrow & 20x-10& = &-7+14+3x \\\Leftrightarrow & 20x \color{red}{-10} & = &7 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 20x-3x& = &7+10 \\\Leftrightarrow & 17x& = &17 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{17}{ \color{red}{17} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-3)& = & -7 \color{red}{+} (10+4x) \\\Leftrightarrow & -15x-9& = &-7+10+4x \\\Leftrightarrow & -15x \color{red}{-9} & = &3 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & -15x-4x& = &3+9 \\\Leftrightarrow & -19x& = &12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-12}{19} & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-5x-7)& = & 1 \color{red}{-} (-14+x) \\\Leftrightarrow & -25x-35& = &1+14-x \\\Leftrightarrow & -25x \color{red}{-35} & = &15 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -25x+x& = &15+35 \\\Leftrightarrow & -24x& = &50 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{50}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{-25}{12} & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x+4)& = & -3 \color{red}{+} (1+x) \\\Leftrightarrow & -12x+12& = &-3+1+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-2-12 \\\Leftrightarrow & -13x& = &-14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x+4)& = & -11 \color{red}{-} (7+x) \\\Leftrightarrow & -24x+16& = &-11-7-x \\\Leftrightarrow & -24x \color{red}{+16} & = &-18 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &-18-16 \\\Leftrightarrow & -23x& = &-34 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-34}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{34}{23} & & \\ & V = \left\{ \frac{34}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x-6)& = & 13 \color{red}{-} (-7+3x) \\\Leftrightarrow & 2x-12& = &13+7-3x \\\Leftrightarrow & 2x \color{red}{-12} & = &20 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 2x+3x& = &20+12 \\\Leftrightarrow & 5x& = &32 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{32}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{32}{5} & & \\ & V = \left\{ \frac{32}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x+5)& = & 15 \color{red}{-} (9+x) \\\Leftrightarrow & -12x+20& = &15-9-x \\\Leftrightarrow & -12x \color{red}{+20} & = &6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -12x+x& = &6-20 \\\Leftrightarrow & -11x& = &-14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)