Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x+3)& = & -2 \color{red}{+} (9-5x) \\\Leftrightarrow & 16x+12& = &-2+9-5x \\\Leftrightarrow & 16x \color{red}{+12} & = &7 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 16x+5x& = &7-12 \\\Leftrightarrow & 21x& = &-5 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-5}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{21} & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (2x+1)& = & -9 \color{red}{-} (-14+x) \\\Leftrightarrow & 4x+2& = &-9+14-x \\\Leftrightarrow & 4x \color{red}{+2} & = &5 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 4x+x& = &5-2 \\\Leftrightarrow & 5x& = &3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-5)& = & 12 \color{red}{-} (-9+3x) \\\Leftrightarrow & 4x-10& = &12+9-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &21 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &21+10 \\\Leftrightarrow & 7x& = &31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{31}{7} & & \\ & V = \left\{ \frac{31}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x+1)& = & 11 \color{red}{-} (9-2x) \\\Leftrightarrow & -15x+3& = &11-9+2x \\\Leftrightarrow & -15x \color{red}{+3} & = &2 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -15x-2x& = &2-3 \\\Leftrightarrow & -17x& = &-1 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-1}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{1}{17} & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x-7)& = & 9 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x-14& = &9-8+x \\\Leftrightarrow & 12x \color{red}{-14} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &1+14 \\\Leftrightarrow & 11x& = &15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x-6)& = & 1 \color{red}{-} (6+x) \\\Leftrightarrow & 12x-24& = &1-6-x \\\Leftrightarrow & 12x \color{red}{-24} & = &-5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &-5+24 \\\Leftrightarrow & 13x& = &19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+5)& = & 5 \color{red}{+} (-2+4x) \\\Leftrightarrow & -3x+15& = &5-2+4x \\\Leftrightarrow & -3x \color{red}{+15} & = &3 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -3x-4x& = &3-15 \\\Leftrightarrow & -7x& = &-12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x+7)& = & 3 \color{red}{+} (-14+x) \\\Leftrightarrow & -2x+14& = &3-14+x \\\Leftrightarrow & -2x \color{red}{+14} & = &-11 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -2x-x& = &-11-14 \\\Leftrightarrow & -3x& = &-25 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-25}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{25}{3} & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x+3)& = & -15 \color{red}{+} (-10-3x) \\\Leftrightarrow & 10x+6& = &-15-10-3x \\\Leftrightarrow & 10x \color{red}{+6} & = &-25 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 10x+3x& = &-25-6 \\\Leftrightarrow & 13x& = &-31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-31}{13} & & \\ & V = \left\{ \frac{-31}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x+3)& = & -2 \color{red}{+} (-2+3x) \\\Leftrightarrow & -20x+15& = &-2-2+3x \\\Leftrightarrow & -20x \color{red}{+15} & = &-4 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & -20x-3x& = &-4-15 \\\Leftrightarrow & -23x& = &-19 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-19}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x+3)& = & -8 \color{red}{+} (4+x) \\\Leftrightarrow & 4x+6& = &-8+4+x \\\Leftrightarrow & 4x \color{red}{+6} & = &-4 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 4x-x& = &-4-6 \\\Leftrightarrow & 3x& = &-10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x-7)& = & 10 \color{red}{-} (11+4x) \\\Leftrightarrow & -15x-21& = &10-11-4x \\\Leftrightarrow & -15x \color{red}{-21} & = &-1 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & -15x+4x& = &-1+21 \\\Leftrightarrow & -11x& = &20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)