Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+5)& = & 7 \color{red}{+} (8+x) \\\Leftrightarrow & -12x+10& = &7+8+x \\\Leftrightarrow & -12x \color{red}{+10} & = &15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -12x-x& = &15-10 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x-3)& = & -4 \color{red}{+} (13+x) \\\Leftrightarrow & 30x-15& = &-4+13+x \\\Leftrightarrow & 30x \color{red}{-15} & = &9 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 30x-x& = &9+15 \\\Leftrightarrow & 29x& = &24 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{24}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{24}{29} & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x-5)& = & -14 \color{red}{+} (13-5x) \\\Leftrightarrow & 6x-30& = &-14+13-5x \\\Leftrightarrow & 6x \color{red}{-30} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & 6x+5x& = &-1+30 \\\Leftrightarrow & 11x& = &29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-5)& = & 1 \color{red}{+} (-2+x) \\\Leftrightarrow & -30x-30& = &1-2+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-1+30 \\\Leftrightarrow & -31x& = &29 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{29}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-29}{31} & & \\ & V = \left\{ \frac{-29}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x-2)& = & 3 \color{red}{-} (-11-3x) \\\Leftrightarrow & -10x-10& = &3+11+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &14 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &14+10 \\\Leftrightarrow & -13x& = &24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x-4)& = & -6 \color{red}{-} (-5-3x) \\\Leftrightarrow & -10x-20& = &-6+5+3x \\\Leftrightarrow & -10x \color{red}{-20} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -10x-3x& = &-1+20 \\\Leftrightarrow & -13x& = &19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+1)& = & -14 \color{red}{-} (7-4x) \\\Leftrightarrow & -5x+5& = &-14-7+4x \\\Leftrightarrow & -5x \color{red}{+5} & = &-21 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &-21 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & -5x-4x& = &-21-5 \\\Leftrightarrow & -9x& = &-26 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-26}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{26}{9} & & \\ & V = \left\{ \frac{26}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-4)& = & 9 \color{red}{+} (4+x) \\\Leftrightarrow & -3x-12& = &9+4+x \\\Leftrightarrow & -3x \color{red}{-12} & = &13 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -3x-x& = &13+12 \\\Leftrightarrow & -4x& = &25 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{25}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-25}{4} & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-2)& = & 13 \color{red}{+} (6+x) \\\Leftrightarrow & -12x-4& = &13+6+x \\\Leftrightarrow & -12x \color{red}{-4} & = &19 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &19+4 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x+1)& = & -3 \color{red}{+} (9-3x) \\\Leftrightarrow & 16x+4& = &-3+9-3x \\\Leftrightarrow & 16x \color{red}{+4} & = &6 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 16x+3x& = &6-4 \\\Leftrightarrow & 19x& = &2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-2x+7)& = & 13 \color{red}{-} (6-3x) \\\Leftrightarrow & -10x+35& = &13-6+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &7 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &7-35 \\\Leftrightarrow & -13x& = &-28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+6)& = & 8 \color{red}{+} (-3+3x) \\\Leftrightarrow & -16x+24& = &8-3+3x \\\Leftrightarrow & -16x \color{red}{+24} & = &5 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -16x-3x& = &5-24 \\\Leftrightarrow & -19x& = &-19 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-19}{ \color{red}{-19} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)