Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(-4x-2)=-7-(5+x)\)
2. \(2(5x+7)=1-(1+3x)\)
3. \(2(4x+6)=7+(-11+x)\)
4. \(4(x+2)=14-(14+3x)\)
5. \(6(2x-3)=-15-(5+x)\)
6. \(4(-2x+7)=8+(-6-5x)\)
7. \(2(5x-2)=-15-(10-3x)\)
8. \(6(5x-4)=11-(6+x)\)
9. \(2(6x-4)=4+(-13+x)\)
10. \(3(-x+5)=1-(11-2x)\)
11. \(6(5x-1)=6-(2+x)\)
12. \(5(6x+4)=5-(-11+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x-2)& = & -7 \color{red}{-} (5+x) \\\Leftrightarrow & -24x-12& = &-7-5-x \\\Leftrightarrow & -24x \color{red}{-12} & = &-12 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &-12+12 \\\Leftrightarrow & -23x& = &0 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{0}{ \color{red}{-23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x+7)& = & 1 \color{red}{-} (1+3x) \\\Leftrightarrow & 10x+14& = &1-1-3x \\\Leftrightarrow & 10x \color{red}{+14} & = &0 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 10x+3x& = &0-14 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+6)& = & 7 \color{red}{+} (-11+x) \\\Leftrightarrow & 8x+12& = &7-11+x \\\Leftrightarrow & 8x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &-4-12 \\\Leftrightarrow & 7x& = &-16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x+2)& = & 14 \color{red}{-} (14+3x) \\\Leftrightarrow & 4x+8& = &14-14-3x \\\Leftrightarrow & 4x \color{red}{+8} & = &0 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 4x+3x& = &0-8 \\\Leftrightarrow & 7x& = &-8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x-3)& = & -15 \color{red}{-} (5+x) \\\Leftrightarrow & 12x-18& = &-15-5-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-20 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-20+18 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x+7)& = & 8 \color{red}{+} (-6-5x) \\\Leftrightarrow & -8x+28& = &8-6-5x \\\Leftrightarrow & -8x \color{red}{+28} & = &2 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & -8x+5x& = &2-28 \\\Leftrightarrow & -3x& = &-26 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-26}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{26}{3} & & \\ & V = \left\{ \frac{26}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x-2)& = & -15 \color{red}{-} (10-3x) \\\Leftrightarrow & 10x-4& = &-15-10+3x \\\Leftrightarrow & 10x \color{red}{-4} & = &-25 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 10x-3x& = &-25+4 \\\Leftrightarrow & 7x& = &-21 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-21}{ \color{red}{7} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x-4)& = & 11 \color{red}{-} (6+x) \\\Leftrightarrow & 30x-24& = &11-6-x \\\Leftrightarrow & 30x \color{red}{-24} & = &5 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 30x+x& = &5+24 \\\Leftrightarrow & 31x& = &29 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{29}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{29}{31} & & \\ & V = \left\{ \frac{29}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x-4)& = & 4 \color{red}{+} (-13+x) \\\Leftrightarrow & 12x-8& = &4-13+x \\\Leftrightarrow & 12x \color{red}{-8} & = &-9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &-9+8 \\\Leftrightarrow & 11x& = &-1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x+5)& = & 1 \color{red}{-} (11-2x) \\\Leftrightarrow & -3x+15& = &1-11+2x \\\Leftrightarrow & -3x \color{red}{+15} & = &-10 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -3x-2x& = &-10-15 \\\Leftrightarrow & -5x& = &-25 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-25}{ \color{red}{-5} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x-1)& = & 6 \color{red}{-} (2+x) \\\Leftrightarrow & 30x-6& = &6-2-x \\\Leftrightarrow & 30x \color{red}{-6} & = &4 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &4+6 \\\Leftrightarrow & 31x& = &10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+4)& = & 5 \color{red}{-} (-11+x) \\\Leftrightarrow & 30x+20& = &5+11-x \\\Leftrightarrow & 30x \color{red}{+20} & = &16 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 30x+x& = &16-20 \\\Leftrightarrow & 31x& = &-4 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-4}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-4}{31} & & \\ & V = \left\{ \frac{-4}{31} \right\} & \\\end{align}\)