Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+2)& = & -7 \color{red}{+} (-4+x) \\\Leftrightarrow & 10x+4& = &-7-4+x \\\Leftrightarrow & 10x \color{red}{+4} & = &-11 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 10x-x& = &-11-4 \\\Leftrightarrow & 9x& = &-15 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-15}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x+5)& = & 13 \color{red}{+} (-8+x) \\\Leftrightarrow & 15x+15& = &13-8+x \\\Leftrightarrow & 15x \color{red}{+15} & = &5 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 15x-x& = &5-15 \\\Leftrightarrow & 14x& = &-10 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-10}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+4)& = & 8 \color{red}{-} (-14+4x) \\\Leftrightarrow & 15x+20& = &8+14-4x \\\Leftrightarrow & 15x \color{red}{+20} & = &22 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & 15x+4x& = &22-20 \\\Leftrightarrow & 19x& = &2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x-3)& = & 12 \color{red}{+} (6-3x) \\\Leftrightarrow & 10x-15& = &12+6-3x \\\Leftrightarrow & 10x \color{red}{-15} & = &18 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & 10x+3x& = &18+15 \\\Leftrightarrow & 13x& = &33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x+1)& = & 12 \color{red}{-} (10+x) \\\Leftrightarrow & -24x+6& = &12-10-x \\\Leftrightarrow & -24x \color{red}{+6} & = &2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &2-6 \\\Leftrightarrow & -23x& = &-4 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-4}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x-7)& = & -11 \color{red}{+} (-3-2x) \\\Leftrightarrow & -15x-35& = &-11-3-2x \\\Leftrightarrow & -15x \color{red}{-35} & = &-14 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &-14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & -15x+2x& = &-14+35 \\\Leftrightarrow & -13x& = &21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+5)& = & -7 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x+30& = &-7+4-x \\\Leftrightarrow & -12x \color{red}{+30} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -12x+x& = &-3-30 \\\Leftrightarrow & -11x& = &-33 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-33}{ \color{red}{-11} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-3)& = & 7 \color{red}{-} (1-2x) \\\Leftrightarrow & -3x-9& = &7-1+2x \\\Leftrightarrow & -3x \color{red}{-9} & = &6 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & -3x-2x& = &6+9 \\\Leftrightarrow & -5x& = &15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{15}{ \color{red}{-5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x+3)& = & -13 \color{red}{+} (-14+x) \\\Leftrightarrow & 4x+6& = &-13-14+x \\\Leftrightarrow & 4x \color{red}{+6} & = &-27 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 4x-x& = &-27-6 \\\Leftrightarrow & 3x& = &-33 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-33}{ \color{red}{3} } \\\Leftrightarrow & x = -11 & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x-6)& = & -12 \color{red}{-} (4+x) \\\Leftrightarrow & 30x-30& = &-12-4-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-16 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-16+30 \\\Leftrightarrow & 31x& = &14 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{14}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{14}{31} & & \\ & V = \left\{ \frac{14}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-1)& = & -5 \color{red}{-} (-12-5x) \\\Leftrightarrow & -3x-3& = &-5+12+5x \\\Leftrightarrow & -3x \color{red}{-3} & = &7 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -3x-5x& = &7+3 \\\Leftrightarrow & -8x& = &10 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{10}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-5}{4} & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x-5)& = & 13 \color{red}{-} (4-2x) \\\Leftrightarrow & 15x-15& = &13-4+2x \\\Leftrightarrow & 15x \color{red}{-15} & = &9 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 15x-2x& = &9+15 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)