Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+7)& = & -8 \color{red}{-} (-8+x) \\\Leftrightarrow & 6x+42& = &-8+8-x \\\Leftrightarrow & 6x \color{red}{+42} & = &0 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 6x+x& = &0-42 \\\Leftrightarrow & 7x& = &-42 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-42}{ \color{red}{7} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x-1)& = & 4 \color{red}{+} (14+x) \\\Leftrightarrow & -6x-2& = &4+14+x \\\Leftrightarrow & -6x \color{red}{-2} & = &18 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -6x-x& = &18+2 \\\Leftrightarrow & -7x& = &20 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{20}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x-5)& = & 13 \color{red}{-} (7+x) \\\Leftrightarrow & -24x-30& = &13-7-x \\\Leftrightarrow & -24x \color{red}{-30} & = &6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -24x+x& = &6+30 \\\Leftrightarrow & -23x& = &36 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{36}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-36}{23} & & \\ & V = \left\{ \frac{-36}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-x-1)& = & -5 \color{red}{-} (15+4x) \\\Leftrightarrow & -3x-3& = &-5-15-4x \\\Leftrightarrow & -3x \color{red}{-3} & = &-20 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{+4x} & = &-20 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+3} \\\Leftrightarrow & -3x+4x& = &-20+3 \\\Leftrightarrow & x& = &-17 \\ & V = \left\{ -17 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x+6)& = & -2 \color{red}{-} (15+3x) \\\Leftrightarrow & -4x+24& = &-2-15-3x \\\Leftrightarrow & -4x \color{red}{+24} & = &-17 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -4x+3x& = &-17-24 \\\Leftrightarrow & -x& = &-41 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-41}{ \color{red}{-1} } \\\Leftrightarrow & x = 41 & & \\ & V = \left\{ 41 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-2)& = & 4 \color{red}{-} (-12+x) \\\Leftrightarrow & -24x-8& = &4+12-x \\\Leftrightarrow & -24x \color{red}{-8} & = &16 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &16+8 \\\Leftrightarrow & -23x& = &24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x-5)& = & 13 \color{red}{+} (1+2x) \\\Leftrightarrow & -3x-15& = &13+1+2x \\\Leftrightarrow & -3x \color{red}{-15} & = &14 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -3x-2x& = &14+15 \\\Leftrightarrow & -5x& = &29 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{29}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-29}{5} & & \\ & V = \left\{ \frac{-29}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x-3)& = & 3 \color{red}{-} (3+x) \\\Leftrightarrow & -24x-18& = &3-3-x \\\Leftrightarrow & -24x \color{red}{-18} & = &0 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -24x+x& = &0+18 \\\Leftrightarrow & -23x& = &18 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{18}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-18}{23} & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x-3)& = & -13 \color{red}{+} (15-5x) \\\Leftrightarrow & -6x-9& = &-13+15-5x \\\Leftrightarrow & -6x \color{red}{-9} & = &2 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & -6x+5x& = &2+9 \\\Leftrightarrow & -x& = &11 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{11}{ \color{red}{-1} } \\\Leftrightarrow & x = -11 & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x-1)& = & 11 \color{red}{-} (2+x) \\\Leftrightarrow & -12x-6& = &11-2-x \\\Leftrightarrow & -12x \color{red}{-6} & = &9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &9+6 \\\Leftrightarrow & -11x& = &15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (2x-5)& = & -3 \color{red}{-} (-11+x) \\\Leftrightarrow & 10x-25& = &-3+11-x \\\Leftrightarrow & 10x \color{red}{-25} & = &8 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 10x+x& = &8+25 \\\Leftrightarrow & 11x& = &33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{33}{ \color{red}{11} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+5)& = & 3 \color{red}{-} (6+x) \\\Leftrightarrow & 12x+30& = &3-6-x \\\Leftrightarrow & 12x \color{red}{+30} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 12x+x& = &-3-30 \\\Leftrightarrow & 13x& = &-33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-33}{13} & & \\ & V = \left\{ \frac{-33}{13} \right\} & \\\end{align}\)