Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x+6)& = & 7 \color{red}{+} (-5-3x) \\\Leftrightarrow & 16x+24& = &7-5-3x \\\Leftrightarrow & 16x \color{red}{+24} & = &2 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & 16x+3x& = &2-24 \\\Leftrightarrow & 19x& = &-22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-22}{19} & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-4)& = & -7 \color{red}{+} (-6+x) \\\Leftrightarrow & 15x-12& = &-7-6+x \\\Leftrightarrow & 15x \color{red}{-12} & = &-13 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 15x-x& = &-13+12 \\\Leftrightarrow & 14x& = &-1 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-1}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-1}{14} & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x-1)& = & 2 \color{red}{-} (-4-5x) \\\Leftrightarrow & 8x-2& = &2+4+5x \\\Leftrightarrow & 8x \color{red}{-2} & = &6 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & 8x-5x& = &6+2 \\\Leftrightarrow & 3x& = &8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (2x-1)& = & -12 \color{red}{-} (10+3x) \\\Leftrightarrow & 8x-4& = &-12-10-3x \\\Leftrightarrow & 8x \color{red}{-4} & = &-22 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 8x+3x& = &-22+4 \\\Leftrightarrow & 11x& = &-18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x-3)& = & 14 \color{red}{-} (11+2x) \\\Leftrightarrow & -15x-9& = &14-11-2x \\\Leftrightarrow & -15x \color{red}{-9} & = &3 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+9} \\\Leftrightarrow & -15x+2x& = &3+9 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+4)& = & 6 \color{red}{+} (14+4x) \\\Leftrightarrow & 5x+20& = &6+14+4x \\\Leftrightarrow & 5x \color{red}{+20} & = &20 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &20 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & 5x-4x& = &20-20 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x+3)& = & 15 \color{red}{+} (6+2x) \\\Leftrightarrow & 25x+15& = &15+6+2x \\\Leftrightarrow & 25x \color{red}{+15} & = &21 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &21 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 25x-2x& = &21-15 \\\Leftrightarrow & 23x& = &6 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{6}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x+4)& = & 7 \color{red}{-} (7-5x) \\\Leftrightarrow & -6x+8& = &7-7+5x \\\Leftrightarrow & -6x \color{red}{+8} & = &0 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & -6x-5x& = &0-8 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x+6)& = & 15 \color{red}{+} (-7+3x) \\\Leftrightarrow & -10x+30& = &15-7+3x \\\Leftrightarrow & -10x \color{red}{+30} & = &8 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & -10x-3x& = &8-30 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-7)& = & 5 \color{red}{-} (-5-3x) \\\Leftrightarrow & 4x-28& = &5+5+3x \\\Leftrightarrow & 4x \color{red}{-28} & = &10 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & 4x-3x& = &10+28 \\\Leftrightarrow & x& = &38 \\ & V = \left\{ 38 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-6)& = & -5 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x-24& = &-5+6-x \\\Leftrightarrow & -24x \color{red}{-24} & = &1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &1+24 \\\Leftrightarrow & -23x& = &25 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{25}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-25}{23} & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x-3)& = & 14 \color{red}{+} (4-3x) \\\Leftrightarrow & 4x-12& = &14+4-3x \\\Leftrightarrow & 4x \color{red}{-12} & = &18 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 4x+3x& = &18+12 \\\Leftrightarrow & 7x& = &30 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{30}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{30}{7} & & \\ & V = \left\{ \frac{30}{7} \right\} & \\\end{align}\)