Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+4)& = & -7 \color{red}{-} (11-4x) \\\Leftrightarrow & -9x+12& = &-7-11+4x \\\Leftrightarrow & -9x \color{red}{+12} & = &-18 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &-18 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & -9x-4x& = &-18-12 \\\Leftrightarrow & -13x& = &-30 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-30}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x+7)& = & -2 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x+28& = &-2+15-x \\\Leftrightarrow & 12x \color{red}{+28} & = &13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 12x+x& = &13-28 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (2x+1)& = & -15 \color{red}{+} (12+x) \\\Leftrightarrow & 12x+6& = &-15+12+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-3-6 \\\Leftrightarrow & 11x& = &-9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x+1)& = & 8 \color{red}{-} (-11+x) \\\Leftrightarrow & 9x+3& = &8+11-x \\\Leftrightarrow & 9x \color{red}{+3} & = &19 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 9x+x& = &19-3 \\\Leftrightarrow & 10x& = &16 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{16}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x+7)& = & 8 \color{red}{-} (1-5x) \\\Leftrightarrow & 36x+42& = &8-1+5x \\\Leftrightarrow & 36x \color{red}{+42} & = &7 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-42} \\\Leftrightarrow & 36x-5x& = &7-42 \\\Leftrightarrow & 31x& = &-35 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-35}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-35}{31} & & \\ & V = \left\{ \frac{-35}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x+6)& = & -12 \color{red}{+} (14-2x) \\\Leftrightarrow & -5x+30& = &-12+14-2x \\\Leftrightarrow & -5x \color{red}{+30} & = &2 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & -5x+2x& = &2-30 \\\Leftrightarrow & -3x& = &-28 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-28}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{28}{3} & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x-4)& = & 7 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x-8& = &7+14-x \\\Leftrightarrow & 12x \color{red}{-8} & = &21 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &21+8 \\\Leftrightarrow & 13x& = &29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{29}{13} & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-3)& = & 13 \color{red}{+} (15+x) \\\Leftrightarrow & 3x-9& = &13+15+x \\\Leftrightarrow & 3x \color{red}{-9} & = &28 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 3x-x& = &28+9 \\\Leftrightarrow & 2x& = &37 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{37}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{37}{2} & & \\ & V = \left\{ \frac{37}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x-4)& = & -4 \color{red}{-} (-2+3x) \\\Leftrightarrow & -8x-8& = &-4+2-3x \\\Leftrightarrow & -8x \color{red}{-8} & = &-2 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -8x+3x& = &-2+8 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x+6)& = & 7 \color{red}{+} (-2-5x) \\\Leftrightarrow & -6x+18& = &7-2-5x \\\Leftrightarrow & -6x \color{red}{+18} & = &5 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -6x+5x& = &5-18 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x-5)& = & 13 \color{red}{-} (-1+3x) \\\Leftrightarrow & -16x-20& = &13+1-3x \\\Leftrightarrow & -16x \color{red}{-20} & = &14 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -16x+3x& = &14+20 \\\Leftrightarrow & -13x& = &34 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{34}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-34}{13} & & \\ & V = \left\{ \frac{-34}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x-4)& = & -1 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x-12& = &-1-6+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-7+12 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)