Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x-6)& = & 10 \color{red}{-} (12-4x) \\\Leftrightarrow & 5x-30& = &10-12+4x \\\Leftrightarrow & 5x \color{red}{-30} & = &-2 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &-2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & 5x-4x& = &-2+30 \\\Leftrightarrow & x& = &28 \\ & V = \left\{ 28 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (6x+1)& = & 13 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+2& = &13-14+x \\\Leftrightarrow & 12x \color{red}{+2} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 12x-x& = &-1-2 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-4)& = & -2 \color{red}{+} (-3+x) \\\Leftrightarrow & 18x-24& = &-2-3+x \\\Leftrightarrow & 18x \color{red}{-24} & = &-5 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 18x-x& = &-5+24 \\\Leftrightarrow & 17x& = &19 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{19}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{19}{17} & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x-1)& = & 12 \color{red}{+} (-13-3x) \\\Leftrightarrow & 10x-2& = &12-13-3x \\\Leftrightarrow & 10x \color{red}{-2} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 10x+3x& = &-1+2 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x-5)& = & -4 \color{red}{-} (13+x) \\\Leftrightarrow & -6x-10& = &-4-13-x \\\Leftrightarrow & -6x \color{red}{-10} & = &-17 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -6x+x& = &-17+10 \\\Leftrightarrow & -5x& = &-7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x-3)& = & 15 \color{red}{+} (-10-5x) \\\Leftrightarrow & 6x-6& = &15-10-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &5 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &5+6 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+1)& = & 10 \color{red}{+} (13-3x) \\\Leftrightarrow & -4x+2& = &10+13-3x \\\Leftrightarrow & -4x \color{red}{+2} & = &23 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -4x+3x& = &23-2 \\\Leftrightarrow & -x& = &21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{21}{ \color{red}{-1} } \\\Leftrightarrow & x = -21 & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x-3)& = & 6 \color{red}{-} (-8-3x) \\\Leftrightarrow & 4x-12& = &6+8+3x \\\Leftrightarrow & 4x \color{red}{-12} & = &14 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 4x-3x& = &14+12 \\\Leftrightarrow & x& = &26 \\ & V = \left\{ 26 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x-5)& = & -14 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x-30& = &-14-5+x \\\Leftrightarrow & -12x \color{red}{-30} & = &-19 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -12x-x& = &-19+30 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-2)& = & 10 \color{red}{-} (-10+x) \\\Leftrightarrow & 20x-8& = &10+10-x \\\Leftrightarrow & 20x \color{red}{-8} & = &20 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 20x+x& = &20+8 \\\Leftrightarrow & 21x& = &28 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{28}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x+4)& = & 7 \color{red}{+} (-11+x) \\\Leftrightarrow & -20x+20& = &7-11+x \\\Leftrightarrow & -20x \color{red}{+20} & = &-4 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &-4-20 \\\Leftrightarrow & -21x& = &-24 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-24}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-x+7)& = & 2 \color{red}{-} (9-2x) \\\Leftrightarrow & -3x+21& = &2-9+2x \\\Leftrightarrow & -3x \color{red}{+21} & = &-7 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &-7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & -3x-2x& = &-7-21 \\\Leftrightarrow & -5x& = &-28 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-28}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{28}{5} & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)