Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+2)& = & -14 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x+8& = &-14+15-x \\\Leftrightarrow & 12x \color{red}{+8} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &1-8 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-2)& = & -7 \color{red}{-} (-9-4x) \\\Leftrightarrow & 5x-10& = &-7+9+4x \\\Leftrightarrow & 5x \color{red}{-10} & = &2 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & 5x-4x& = &2+10 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+3)& = & -13 \color{red}{+} (-4+x) \\\Leftrightarrow & 12x+6& = &-13-4+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-17-6 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x-3)& = & -11 \color{red}{+} (6+x) \\\Leftrightarrow & -30x-15& = &-11+6+x \\\Leftrightarrow & -30x \color{red}{-15} & = &-5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -30x-x& = &-5+15 \\\Leftrightarrow & -31x& = &10 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{10}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-10}{31} & & \\ & V = \left\{ \frac{-10}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+2)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & -30x+10& = &8-4+x \\\Leftrightarrow & -30x \color{red}{+10} & = &4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -30x-x& = &4-10 \\\Leftrightarrow & -31x& = &-6 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-6}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+4)& = & 2 \color{red}{-} (12+x) \\\Leftrightarrow & -24x+16& = &2-12-x \\\Leftrightarrow & -24x \color{red}{+16} & = &-10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &-10-16 \\\Leftrightarrow & -23x& = &-26 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-26}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{26}{23} & & \\ & V = \left\{ \frac{26}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-5)& = & -2 \color{red}{-} (3+x) \\\Leftrightarrow & 20x-25& = &-2-3-x \\\Leftrightarrow & 20x \color{red}{-25} & = &-5 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 20x+x& = &-5+25 \\\Leftrightarrow & 21x& = &20 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{20}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x-5)& = & 5 \color{red}{+} (8-2x) \\\Leftrightarrow & 5x-25& = &5+8-2x \\\Leftrightarrow & 5x \color{red}{-25} & = &13 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & 5x+2x& = &13+25 \\\Leftrightarrow & 7x& = &38 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{38}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{38}{7} & & \\ & V = \left\{ \frac{38}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x-3)& = & 7 \color{red}{+} (-3+x) \\\Leftrightarrow & 24x-12& = &7-3+x \\\Leftrightarrow & 24x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &4+12 \\\Leftrightarrow & 23x& = &16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x+3)& = & -3 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x+12& = &-3+11-x \\\Leftrightarrow & -24x \color{red}{+12} & = &8 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &8-12 \\\Leftrightarrow & -23x& = &-4 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-4}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-2x+7)& = & -15 \color{red}{-} (-6+x) \\\Leftrightarrow & -6x+21& = &-15+6-x \\\Leftrightarrow & -6x \color{red}{+21} & = &-9 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -6x+x& = &-9-21 \\\Leftrightarrow & -5x& = &-30 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-30}{ \color{red}{-5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x+1)& = & 5 \color{red}{+} (9+x) \\\Leftrightarrow & 12x+4& = &5+9+x \\\Leftrightarrow & 12x \color{red}{+4} & = &14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &14-4 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)