Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x+1)& = & 3 \color{red}{-} (12+x) \\\Leftrightarrow & 5x+5& = &3-12-x \\\Leftrightarrow & 5x \color{red}{+5} & = &-9 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 5x+x& = &-9-5 \\\Leftrightarrow & 6x& = &-14 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-14}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x+5)& = & 15 \color{red}{-} (6+x) \\\Leftrightarrow & -20x+20& = &15-6-x \\\Leftrightarrow & -20x \color{red}{+20} & = &9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -20x+x& = &9-20 \\\Leftrightarrow & -19x& = &-11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x+7)& = & 15 \color{red}{+} (-5+x) \\\Leftrightarrow & -6x+21& = &15-5+x \\\Leftrightarrow & -6x \color{red}{+21} & = &10 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -6x-x& = &10-21 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x+5)& = & 8 \color{red}{-} (-9-5x) \\\Leftrightarrow & 8x+10& = &8+9+5x \\\Leftrightarrow & 8x \color{red}{+10} & = &17 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & 8x-5x& = &17-10 \\\Leftrightarrow & 3x& = &7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-6)& = & -2 \color{red}{+} (-4-2x) \\\Leftrightarrow & 15x-30& = &-2-4-2x \\\Leftrightarrow & 15x \color{red}{-30} & = &-6 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &-6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & 15x+2x& = &-6+30 \\\Leftrightarrow & 17x& = &24 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{24}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{24}{17} & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-5)& = & 12 \color{red}{+} (1+x) \\\Leftrightarrow & -24x-20& = &12+1+x \\\Leftrightarrow & -24x \color{red}{-20} & = &13 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -24x-x& = &13+20 \\\Leftrightarrow & -25x& = &33 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{33}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-33}{25} & & \\ & V = \left\{ \frac{-33}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x-2)& = & -10 \color{red}{+} (-3+x) \\\Leftrightarrow & 12x-8& = &-10-3+x \\\Leftrightarrow & 12x \color{red}{-8} & = &-13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &-13+8 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x+6)& = & 3 \color{red}{-} (3+x) \\\Leftrightarrow & -9x+18& = &3-3-x \\\Leftrightarrow & -9x \color{red}{+18} & = &0 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -9x+x& = &0-18 \\\Leftrightarrow & -8x& = &-18 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-18}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{9}{4} & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x-2)& = & 12 \color{red}{+} (5-5x) \\\Leftrightarrow & -36x-12& = &12+5-5x \\\Leftrightarrow & -36x \color{red}{-12} & = &17 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -36x+5x& = &17+12 \\\Leftrightarrow & -31x& = &29 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{29}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-29}{31} & & \\ & V = \left\{ \frac{-29}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x+1)& = & -14 \color{red}{-} (11+3x) \\\Leftrightarrow & 4x+2& = &-14-11-3x \\\Leftrightarrow & 4x \color{red}{+2} & = &-25 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 4x+3x& = &-25-2 \\\Leftrightarrow & 7x& = &-27 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-27}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x+2)& = & -4 \color{red}{-} (-1+x) \\\Leftrightarrow & 2x+4& = &-4+1-x \\\Leftrightarrow & 2x \color{red}{+4} & = &-3 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &-3-4 \\\Leftrightarrow & 3x& = &-7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x-2)& = & -13 \color{red}{-} (6-4x) \\\Leftrightarrow & -5x-10& = &-13-6+4x \\\Leftrightarrow & -5x \color{red}{-10} & = &-19 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &-19 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -5x-4x& = &-19+10 \\\Leftrightarrow & -9x& = &-9 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-9}{ \color{red}{-9} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)