Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-7)& = & -15 \color{red}{+} (12+x) \\\Leftrightarrow & 2x-14& = &-15+12+x \\\Leftrightarrow & 2x \color{red}{-14} & = &-3 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 2x-x& = &-3+14 \\\Leftrightarrow & x& = &11 \\ & V = \left\{ 11 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x-3)& = & 8 \color{red}{+} (-5-5x) \\\Leftrightarrow & -6x-18& = &8-5-5x \\\Leftrightarrow & -6x \color{red}{-18} & = &3 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -6x+5x& = &3+18 \\\Leftrightarrow & -x& = &21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{21}{ \color{red}{-1} } \\\Leftrightarrow & x = -21 & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-6)& = & -7 \color{red}{+} (15+x) \\\Leftrightarrow & -4x-24& = &-7+15+x \\\Leftrightarrow & -4x \color{red}{-24} & = &8 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -4x-x& = &8+24 \\\Leftrightarrow & -5x& = &32 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{32}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-32}{5} & & \\ & V = \left\{ \frac{-32}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x+6)& = & -4 \color{red}{+} (-14+x) \\\Leftrightarrow & 30x+30& = &-4-14+x \\\Leftrightarrow & 30x \color{red}{+30} & = &-18 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 30x-x& = &-18-30 \\\Leftrightarrow & 29x& = &-48 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-48}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-48}{29} & & \\ & V = \left\{ \frac{-48}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x+1)& = & -3 \color{red}{-} (-7+x) \\\Leftrightarrow & 2x+2& = &-3+7-x \\\Leftrightarrow & 2x \color{red}{+2} & = &4 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 2x+x& = &4-2 \\\Leftrightarrow & 3x& = &2 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{2}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x+1)& = & -5 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x+6& = &-5-2+x \\\Leftrightarrow & -12x \color{red}{+6} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &-7-6 \\\Leftrightarrow & -13x& = &-13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-13}{ \color{red}{-13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x-1)& = & -7 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x-4& = &-7+15-x \\\Leftrightarrow & -12x \color{red}{-4} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &8+4 \\\Leftrightarrow & -11x& = &12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x-3)& = & -6 \color{red}{+} (-3+x) \\\Leftrightarrow & -18x-9& = &-6-3+x \\\Leftrightarrow & -18x \color{red}{-9} & = &-9 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -18x-x& = &-9+9 \\\Leftrightarrow & -19x& = &0 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{0}{ \color{red}{-19} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x+6)& = & 7 \color{red}{-} (-4+x) \\\Leftrightarrow & -10x+12& = &7+4-x \\\Leftrightarrow & -10x \color{red}{+12} & = &11 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -10x+x& = &11-12 \\\Leftrightarrow & -9x& = &-1 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-1}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-2)& = & -15 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x-8& = &-15+8-x \\\Leftrightarrow & -24x \color{red}{-8} & = &-7 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &-7+8 \\\Leftrightarrow & -23x& = &1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-1}{23} & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x-7)& = & 13 \color{red}{+} (5-2x) \\\Leftrightarrow & -5x-35& = &13+5-2x \\\Leftrightarrow & -5x \color{red}{-35} & = &18 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & -5x+2x& = &18+35 \\\Leftrightarrow & -3x& = &53 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{53}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-53}{3} & & \\ & V = \left\{ \frac{-53}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x-2)& = & -6 \color{red}{+} (-10+x) \\\Leftrightarrow & 12x-12& = &-6-10+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-16+12 \\\Leftrightarrow & 11x& = &-4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)