Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-5x-1)& = & 12 \color{red}{+} (-9+3x) \\\Leftrightarrow & -10x-2& = &12-9+3x \\\Leftrightarrow & -10x \color{red}{-2} & = &3 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & -10x-3x& = &3+2 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x+6)& = & -5 \color{red}{+} (1-5x) \\\Leftrightarrow & -18x+36& = &-5+1-5x \\\Leftrightarrow & -18x \color{red}{+36} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -18x+5x& = &-4-36 \\\Leftrightarrow & -13x& = &-40 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-40}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{40}{13} & & \\ & V = \left\{ \frac{40}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-5)& = & -2 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x-15& = &-2-2+x \\\Leftrightarrow & 12x \color{red}{-15} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 12x-x& = &-4+15 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-x+6)& = & 15 \color{red}{+} (-13+2x) \\\Leftrightarrow & -5x+30& = &15-13+2x \\\Leftrightarrow & -5x \color{red}{+30} & = &2 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & -5x-2x& = &2-30 \\\Leftrightarrow & -7x& = &-28 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-28}{ \color{red}{-7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (3x+2)& = & 5 \color{red}{-} (3+x) \\\Leftrightarrow & 9x+6& = &5-3-x \\\Leftrightarrow & 9x \color{red}{+6} & = &2 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 9x+x& = &2-6 \\\Leftrightarrow & 10x& = &-4 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-4}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x+6)& = & 10 \color{red}{+} (-4+x) \\\Leftrightarrow & 9x+18& = &10-4+x \\\Leftrightarrow & 9x \color{red}{+18} & = &6 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 9x-x& = &6-18 \\\Leftrightarrow & 8x& = &-12 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-12}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (2x-2)& = & -4 \color{red}{-} (-11-5x) \\\Leftrightarrow & 6x-6& = &-4+11+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &7 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &7+6 \\\Leftrightarrow & x& = &13 \\ & V = \left\{ 13 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x-6)& = & -15 \color{red}{+} (1+x) \\\Leftrightarrow & -2x-12& = &-15+1+x \\\Leftrightarrow & -2x \color{red}{-12} & = &-14 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -2x-x& = &-14+12 \\\Leftrightarrow & -3x& = &-2 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-2}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x-5)& = & -1 \color{red}{-} (-8+x) \\\Leftrightarrow & 12x-10& = &-1+8-x \\\Leftrightarrow & 12x \color{red}{-10} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 12x+x& = &7+10 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+4)& = & -9 \color{red}{+} (-12-5x) \\\Leftrightarrow & -36x+24& = &-9-12-5x \\\Leftrightarrow & -36x \color{red}{+24} & = &-21 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &-21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -36x+5x& = &-21-24 \\\Leftrightarrow & -31x& = &-45 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-45}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{45}{31} & & \\ & V = \left\{ \frac{45}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x+5)& = & -11 \color{red}{-} (6-5x) \\\Leftrightarrow & -18x+15& = &-11-6+5x \\\Leftrightarrow & -18x \color{red}{+15} & = &-17 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & -18x-5x& = &-17-15 \\\Leftrightarrow & -23x& = &-32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+3)& = & -9 \color{red}{-} (-8-3x) \\\Leftrightarrow & -16x+12& = &-9+8+3x \\\Leftrightarrow & -16x \color{red}{+12} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -16x-3x& = &-1-12 \\\Leftrightarrow & -19x& = &-13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)