Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x+4)& = & 8 \color{red}{-} (4+x) \\\Leftrightarrow & 12x+24& = &8-4-x \\\Leftrightarrow & 12x \color{red}{+24} & = &4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 12x+x& = &4-24 \\\Leftrightarrow & 13x& = &-20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-2)& = & 9 \color{red}{+} (7-3x) \\\Leftrightarrow & -4x-8& = &9+7-3x \\\Leftrightarrow & -4x \color{red}{-8} & = &16 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -4x+3x& = &16+8 \\\Leftrightarrow & -x& = &24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{24}{ \color{red}{-1} } \\\Leftrightarrow & x = -24 & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x+3)& = & -1 \color{red}{-} (-1+x) \\\Leftrightarrow & -30x+15& = &-1+1-x \\\Leftrightarrow & -30x \color{red}{+15} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &0-15 \\\Leftrightarrow & -29x& = &-15 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-15}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{15}{29} & & \\ & V = \left\{ \frac{15}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x+4)& = & 1 \color{red}{+} (-11-3x) \\\Leftrightarrow & 10x+20& = &1-11-3x \\\Leftrightarrow & 10x \color{red}{+20} & = &-10 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 10x+3x& = &-10-20 \\\Leftrightarrow & 13x& = &-30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-30}{13} & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-7)& = & 4 \color{red}{+} (-4-5x) \\\Leftrightarrow & -18x-42& = &4-4-5x \\\Leftrightarrow & -18x \color{red}{-42} & = &0 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & -18x+5x& = &0+42 \\\Leftrightarrow & -13x& = &42 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{42}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-42}{13} & & \\ & V = \left\{ \frac{-42}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x+7)& = & 6 \color{red}{-} (-7+x) \\\Leftrightarrow & -12x+14& = &6+7-x \\\Leftrightarrow & -12x \color{red}{+14} & = &13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -12x+x& = &13-14 \\\Leftrightarrow & -11x& = &-1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-4)& = & 11 \color{red}{+} (5+x) \\\Leftrightarrow & -30x-20& = &11+5+x \\\Leftrightarrow & -30x \color{red}{-20} & = &16 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -30x-x& = &16+20 \\\Leftrightarrow & -31x& = &36 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{36}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-36}{31} & & \\ & V = \left\{ \frac{-36}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x-7)& = & 11 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-14& = &11+7+x \\\Leftrightarrow & 12x \color{red}{-14} & = &18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &18+14 \\\Leftrightarrow & 11x& = &32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x-5)& = & -13 \color{red}{+} (15+x) \\\Leftrightarrow & -4x-10& = &-13+15+x \\\Leftrightarrow & -4x \color{red}{-10} & = &2 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -4x-x& = &2+10 \\\Leftrightarrow & -5x& = &12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x-7)& = & 12 \color{red}{+} (2-2x) \\\Leftrightarrow & -15x-21& = &12+2-2x \\\Leftrightarrow & -15x \color{red}{-21} & = &14 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-21} \color{blue}{+21} \color{blue}{+2x} & = &14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+21} \\\Leftrightarrow & -15x+2x& = &14+21 \\\Leftrightarrow & -13x& = &35 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{35}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-35}{13} & & \\ & V = \left\{ \frac{-35}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-2)& = & -3 \color{red}{+} (-4-5x) \\\Leftrightarrow & 18x-6& = &-3-4-5x \\\Leftrightarrow & 18x \color{red}{-6} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 18x+5x& = &-7+6 \\\Leftrightarrow & 23x& = &-1 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-1}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-1}{23} & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+6)& = & 1 \color{red}{+} (9+x) \\\Leftrightarrow & 6x+18& = &1+9+x \\\Leftrightarrow & 6x \color{red}{+18} & = &10 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 6x-x& = &10-18 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)