Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x-4)& = & -13 \color{red}{+} (-15+x) \\\Leftrightarrow & 8x-16& = &-13-15+x \\\Leftrightarrow & 8x \color{red}{-16} & = &-28 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-28 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 8x-x& = &-28+16 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x-3)& = & -11 \color{red}{+} (-3+x) \\\Leftrightarrow & -8x-6& = &-11-3+x \\\Leftrightarrow & -8x \color{red}{-6} & = &-14 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -8x-x& = &-14+6 \\\Leftrightarrow & -9x& = &-8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x-1)& = & -12 \color{red}{+} (7+x) \\\Leftrightarrow & -2x-2& = &-12+7+x \\\Leftrightarrow & -2x \color{red}{-2} & = &-5 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -2x-x& = &-5+2 \\\Leftrightarrow & -3x& = &-3 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-3}{ \color{red}{-3} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x+6)& = & -3 \color{red}{+} (11+2x) \\\Leftrightarrow & -25x+30& = &-3+11+2x \\\Leftrightarrow & -25x \color{red}{+30} & = &8 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & -25x-2x& = &8-30 \\\Leftrightarrow & -27x& = &-22 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{-22}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{22}{27} & & \\ & V = \left\{ \frac{22}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x+6)& = & 10 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x+12& = &10+5-x \\\Leftrightarrow & -12x \color{red}{+12} & = &15 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &15-12 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x-1)& = & 7 \color{red}{-} (-11-3x) \\\Leftrightarrow & -10x-5& = &7+11+3x \\\Leftrightarrow & -10x \color{red}{-5} & = &18 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-5} \color{blue}{+5} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+5} \\\Leftrightarrow & -10x-3x& = &18+5 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x+2)& = & -2 \color{red}{+} (-1-4x) \\\Leftrightarrow & 5x+10& = &-2-1-4x \\\Leftrightarrow & 5x \color{red}{+10} & = &-3 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & 5x+4x& = &-3-10 \\\Leftrightarrow & 9x& = &-13 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-13}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x+4)& = & -15 \color{red}{-} (-4-5x) \\\Leftrightarrow & -6x+24& = &-15+4+5x \\\Leftrightarrow & -6x \color{red}{+24} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -6x-5x& = &-11-24 \\\Leftrightarrow & -11x& = &-35 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-35}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{35}{11} & & \\ & V = \left\{ \frac{35}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x+2)& = & -12 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x+4& = &-12-8+x \\\Leftrightarrow & -12x \color{red}{+4} & = &-20 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -12x-x& = &-20-4 \\\Leftrightarrow & -13x& = &-24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x+2)& = & 4 \color{red}{-} (9-3x) \\\Leftrightarrow & 10x+10& = &4-9+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-5 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &-5-10 \\\Leftrightarrow & 7x& = &-15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x-4)& = & -11 \color{red}{-} (-12+3x) \\\Leftrightarrow & -8x-16& = &-11+12-3x \\\Leftrightarrow & -8x \color{red}{-16} & = &1 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -8x+3x& = &1+16 \\\Leftrightarrow & -5x& = &17 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{17}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x-7)& = & 8 \color{red}{-} (15+x) \\\Leftrightarrow & 16x-28& = &8-15-x \\\Leftrightarrow & 16x \color{red}{-28} & = &-7 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 16x+x& = &-7+28 \\\Leftrightarrow & 17x& = &21 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{21}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{21}{17} & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)