Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x-1)& = & -12 \color{red}{-} (7+x) \\\Leftrightarrow & 30x-6& = &-12-7-x \\\Leftrightarrow & 30x \color{red}{-6} & = &-19 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &-19+6 \\\Leftrightarrow & 31x& = &-13 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-13}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-13}{31} & & \\ & V = \left\{ \frac{-13}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-7)& = & 2 \color{red}{+} (-4+x) \\\Leftrightarrow & 36x-42& = &2-4+x \\\Leftrightarrow & 36x \color{red}{-42} & = &-2 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 36x-x& = &-2+42 \\\Leftrightarrow & 35x& = &40 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{40}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-x-3)& = & -6 \color{red}{+} (-9+3x) \\\Leftrightarrow & -5x-15& = &-6-9+3x \\\Leftrightarrow & -5x \color{red}{-15} & = &-15 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{-15} \color{blue}{+15} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+15} \\\Leftrightarrow & -5x-3x& = &-15+15 \\\Leftrightarrow & -8x& = &0 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{0}{ \color{red}{-8} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x-1)& = & -5 \color{red}{+} (6+x) \\\Leftrightarrow & -12x-4& = &-5+6+x \\\Leftrightarrow & -12x \color{red}{-4} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &1+4 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x+1)& = & 7 \color{red}{-} (15+x) \\\Leftrightarrow & -8x+4& = &7-15-x \\\Leftrightarrow & -8x \color{red}{+4} & = &-8 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -8x+x& = &-8-4 \\\Leftrightarrow & -7x& = &-12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x-2)& = & -7 \color{red}{+} (6-3x) \\\Leftrightarrow & 25x-10& = &-7+6-3x \\\Leftrightarrow & 25x \color{red}{-10} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 25x+3x& = &-1+10 \\\Leftrightarrow & 28x& = &9 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{9}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{9}{28} & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-3)& = & -10 \color{red}{+} (7+x) \\\Leftrightarrow & -30x-15& = &-10+7+x \\\Leftrightarrow & -30x \color{red}{-15} & = &-3 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -30x-x& = &-3+15 \\\Leftrightarrow & -31x& = &12 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{12}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-12}{31} & & \\ & V = \left\{ \frac{-12}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+6)& = & 11 \color{red}{-} (-4+x) \\\Leftrightarrow & -16x+24& = &11+4-x \\\Leftrightarrow & -16x \color{red}{+24} & = &15 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -16x+x& = &15-24 \\\Leftrightarrow & -15x& = &-9 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-9}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+3)& = & -2 \color{red}{-} (-9+x) \\\Leftrightarrow & 30x+18& = &-2+9-x \\\Leftrightarrow & 30x \color{red}{+18} & = &7 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &7-18 \\\Leftrightarrow & 31x& = &-11 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-11}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-11}{31} & & \\ & V = \left\{ \frac{-11}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x-5)& = & 11 \color{red}{+} (3+3x) \\\Leftrightarrow & -2x-10& = &11+3+3x \\\Leftrightarrow & -2x \color{red}{-10} & = &14 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -2x-3x& = &14+10 \\\Leftrightarrow & -5x& = &24 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{24}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-24}{5} & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+1)& = & -10 \color{red}{+} (6-5x) \\\Leftrightarrow & -36x+6& = &-10+6-5x \\\Leftrightarrow & -36x \color{red}{+6} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -36x+5x& = &-4-6 \\\Leftrightarrow & -31x& = &-10 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-10}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x+5)& = & -13 \color{red}{-} (-8+x) \\\Leftrightarrow & 24x+30& = &-13+8-x \\\Leftrightarrow & 24x \color{red}{+30} & = &-5 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 24x+x& = &-5-30 \\\Leftrightarrow & 25x& = &-35 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-35}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)