Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x-2)& = & 14 \color{red}{+} (-9+x) \\\Leftrightarrow & -15x-10& = &14-9+x \\\Leftrightarrow & -15x \color{red}{-10} & = &5 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -15x-x& = &5+10 \\\Leftrightarrow & -16x& = &15 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{15}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-15}{16} & & \\ & V = \left\{ \frac{-15}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x+6)& = & 10 \color{red}{-} (10+x) \\\Leftrightarrow & -5x+30& = &10-10-x \\\Leftrightarrow & -5x \color{red}{+30} & = &0 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -5x+x& = &0-30 \\\Leftrightarrow & -4x& = &-30 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-30}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{15}{2} & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x-3)& = & 13 \color{red}{-} (15+x) \\\Leftrightarrow & -16x-12& = &13-15-x \\\Leftrightarrow & -16x \color{red}{-12} & = &-2 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -16x+x& = &-2+12 \\\Leftrightarrow & -15x& = &10 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{10}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x-2)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & -24x-12& = &11+3+x \\\Leftrightarrow & -24x \color{red}{-12} & = &14 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &14+12 \\\Leftrightarrow & -25x& = &26 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{26}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-26}{25} & & \\ & V = \left\{ \frac{-26}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x-3)& = & -11 \color{red}{+} (-1+x) \\\Leftrightarrow & -10x-15& = &-11-1+x \\\Leftrightarrow & -10x \color{red}{-15} & = &-12 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -10x-x& = &-12+15 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x-6)& = & -11 \color{red}{+} (-14+x) \\\Leftrightarrow & 6x-12& = &-11-14+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-25 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-25+12 \\\Leftrightarrow & 5x& = &-13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x-3)& = & 12 \color{red}{-} (-13+3x) \\\Leftrightarrow & -4x-6& = &12+13-3x \\\Leftrightarrow & -4x \color{red}{-6} & = &25 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -4x+3x& = &25+6 \\\Leftrightarrow & -x& = &31 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{31}{ \color{red}{-1} } \\\Leftrightarrow & x = -31 & & \\ & V = \left\{ -31 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x+6)& = & -6 \color{red}{+} (4-5x) \\\Leftrightarrow & -6x+36& = &-6+4-5x \\\Leftrightarrow & -6x \color{red}{+36} & = &-2 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -6x+5x& = &-2-36 \\\Leftrightarrow & -x& = &-38 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-38}{ \color{red}{-1} } \\\Leftrightarrow & x = 38 & & \\ & V = \left\{ 38 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-4)& = & -10 \color{red}{+} (-6+x) \\\Leftrightarrow & -18x-12& = &-10-6+x \\\Leftrightarrow & -18x \color{red}{-12} & = &-16 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -18x-x& = &-16+12 \\\Leftrightarrow & -19x& = &-4 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-4}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x+2)& = & -5 \color{red}{+} (13+x) \\\Leftrightarrow & -12x+4& = &-5+13+x \\\Leftrightarrow & -12x \color{red}{+4} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -12x-x& = &8-4 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x-7)& = & 2 \color{red}{+} (13+x) \\\Leftrightarrow & -10x-14& = &2+13+x \\\Leftrightarrow & -10x \color{red}{-14} & = &15 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -10x-x& = &15+14 \\\Leftrightarrow & -11x& = &29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x+6)& = & -3 \color{red}{+} (6+x) \\\Leftrightarrow & 6x+12& = &-3+6+x \\\Leftrightarrow & 6x \color{red}{+12} & = &3 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &3-12 \\\Leftrightarrow & 5x& = &-9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)