Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x+4)& = & 6 \color{red}{-} (-9+x) \\\Leftrightarrow & -15x+12& = &6+9-x \\\Leftrightarrow & -15x \color{red}{+12} & = &15 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -15x+x& = &15-12 \\\Leftrightarrow & -14x& = &3 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{3}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x+5)& = & -10 \color{red}{-} (5-5x) \\\Leftrightarrow & 18x+15& = &-10-5+5x \\\Leftrightarrow & 18x \color{red}{+15} & = &-15 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & 18x-5x& = &-15-15 \\\Leftrightarrow & 13x& = &-30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-30}{13} & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x-7)& = & 10 \color{red}{-} (3+x) \\\Leftrightarrow & 10x-35& = &10-3-x \\\Leftrightarrow & 10x \color{red}{-35} & = &7 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 10x+x& = &7+35 \\\Leftrightarrow & 11x& = &42 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{42}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{42}{11} & & \\ & V = \left\{ \frac{42}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-3)& = & 3 \color{red}{+} (-11-5x) \\\Leftrightarrow & 6x-9& = &3-11-5x \\\Leftrightarrow & 6x \color{red}{-9} & = &-8 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & 6x+5x& = &-8+9 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x+7)& = & 4 \color{red}{-} (-15-3x) \\\Leftrightarrow & 4x+14& = &4+15+3x \\\Leftrightarrow & 4x \color{red}{+14} & = &19 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 4x-3x& = &19-14 \\\Leftrightarrow & x& = &5 \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x-2)& = & 15 \color{red}{+} (2+x) \\\Leftrightarrow & 6x-6& = &15+2+x \\\Leftrightarrow & 6x \color{red}{-6} & = &17 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 6x-x& = &17+6 \\\Leftrightarrow & 5x& = &23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{23}{5} & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-7)& = & -8 \color{red}{-} (-12+4x) \\\Leftrightarrow & -15x-21& = &-8+12-4x \\\Leftrightarrow & -15x \color{red}{-21} & = &4 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & -15x+4x& = &4+21 \\\Leftrightarrow & -11x& = &25 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{25}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-3)& = & -14 \color{red}{+} (-9+x) \\\Leftrightarrow & 20x-12& = &-14-9+x \\\Leftrightarrow & 20x \color{red}{-12} & = &-23 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 20x-x& = &-23+12 \\\Leftrightarrow & 19x& = &-11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x-7)& = & -10 \color{red}{+} (-9-5x) \\\Leftrightarrow & 8x-28& = &-10-9-5x \\\Leftrightarrow & 8x \color{red}{-28} & = &-19 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-28} \color{blue}{+28} \color{blue}{+5x} & = &-19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+28} \\\Leftrightarrow & 8x+5x& = &-19+28 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+5)& = & 7 \color{red}{+} (4+4x) \\\Leftrightarrow & -15x+15& = &7+4+4x \\\Leftrightarrow & -15x \color{red}{+15} & = &11 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -15x-4x& = &11-15 \\\Leftrightarrow & -19x& = &-4 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-4}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x-6)& = & 5 \color{red}{-} (-15-4x) \\\Leftrightarrow & 5x-30& = &5+15+4x \\\Leftrightarrow & 5x \color{red}{-30} & = &20 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &20 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & 5x-4x& = &20+30 \\\Leftrightarrow & x& = &50 \\ & V = \left\{ 50 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+1)& = & -1 \color{red}{-} (8-5x) \\\Leftrightarrow & 8x+2& = &-1-8+5x \\\Leftrightarrow & 8x \color{red}{+2} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 8x-5x& = &-9-2 \\\Leftrightarrow & 3x& = &-11 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-11}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)