Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x+4)& = & 9 \color{red}{-} (7+4x) \\\Leftrightarrow & -15x+20& = &9-7-4x \\\Leftrightarrow & -15x \color{red}{+20} & = &2 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & -15x+4x& = &2-20 \\\Leftrightarrow & -11x& = &-18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-3)& = & 15 \color{red}{-} (-13-5x) \\\Leftrightarrow & 8x-12& = &15+13+5x \\\Leftrightarrow & 8x \color{red}{-12} & = &28 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &28 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 8x-5x& = &28+12 \\\Leftrightarrow & 3x& = &40 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{40}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{40}{3} & & \\ & V = \left\{ \frac{40}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x+3)& = & -3 \color{red}{+} (-8+x) \\\Leftrightarrow & 10x+6& = &-3-8+x \\\Leftrightarrow & 10x \color{red}{+6} & = &-11 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 10x-x& = &-11-6 \\\Leftrightarrow & 9x& = &-17 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-17}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-17}{9} & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x-7)& = & -4 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x-28& = &-4-8+x \\\Leftrightarrow & -12x \color{red}{-28} & = &-12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -12x-x& = &-12+28 \\\Leftrightarrow & -13x& = &16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-5)& = & 7 \color{red}{-} (9-5x) \\\Leftrightarrow & 36x-30& = &7-9+5x \\\Leftrightarrow & 36x \color{red}{-30} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & 36x-5x& = &-2+30 \\\Leftrightarrow & 31x& = &28 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{28}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{28}{31} & & \\ & V = \left\{ \frac{28}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x-1)& = & -3 \color{red}{+} (7+x) \\\Leftrightarrow & 4x-4& = &-3+7+x \\\Leftrightarrow & 4x \color{red}{-4} & = &4 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 4x-x& = &4+4 \\\Leftrightarrow & 3x& = &8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+5)& = & 1 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x+30& = &1+15-x \\\Leftrightarrow & -12x \color{red}{+30} & = &16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -12x+x& = &16-30 \\\Leftrightarrow & -11x& = &-14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x+7)& = & -13 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x+21& = &-13+1-x \\\Leftrightarrow & 12x \color{red}{+21} & = &-12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &-12-21 \\\Leftrightarrow & 13x& = &-33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-33}{13} & & \\ & V = \left\{ \frac{-33}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-4)& = & -13 \color{red}{+} (-15+x) \\\Leftrightarrow & 8x-8& = &-13-15+x \\\Leftrightarrow & 8x \color{red}{-8} & = &-28 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-28 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 8x-x& = &-28+8 \\\Leftrightarrow & 7x& = &-20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x-7)& = & 6 \color{red}{-} (5+x) \\\Leftrightarrow & -12x-42& = &6-5-x \\\Leftrightarrow & -12x \color{red}{-42} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -12x+x& = &1+42 \\\Leftrightarrow & -11x& = &43 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{43}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-43}{11} & & \\ & V = \left\{ \frac{-43}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x+2)& = & -10 \color{red}{-} (5+x) \\\Leftrightarrow & -10x+4& = &-10-5-x \\\Leftrightarrow & -10x \color{red}{+4} & = &-15 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -10x+x& = &-15-4 \\\Leftrightarrow & -9x& = &-19 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-19}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{19}{9} & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x-5)& = & 3 \color{red}{-} (15+x) \\\Leftrightarrow & 6x-15& = &3-15-x \\\Leftrightarrow & 6x \color{red}{-15} & = &-12 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 6x+x& = &-12+15 \\\Leftrightarrow & 7x& = &3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)