Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x+1)& = & 12 \color{red}{+} (-12+x) \\\Leftrightarrow & 3x+3& = &12-12+x \\\Leftrightarrow & 3x \color{red}{+3} & = &0 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 3x-x& = &0-3 \\\Leftrightarrow & 2x& = &-3 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-3}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x-2)& = & 12 \color{red}{-} (-11+x) \\\Leftrightarrow & -25x-10& = &12+11-x \\\Leftrightarrow & -25x \color{red}{-10} & = &23 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -25x+x& = &23+10 \\\Leftrightarrow & -24x& = &33 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{33}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{-11}{8} & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+3)& = & 2 \color{red}{-} (1+x) \\\Leftrightarrow & 20x+12& = &2-1-x \\\Leftrightarrow & 20x \color{red}{+12} & = &1 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 20x+x& = &1-12 \\\Leftrightarrow & 21x& = &-11 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-11}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-11}{21} & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-2x+7)& = & 7 \color{red}{+} (-5-5x) \\\Leftrightarrow & -8x+28& = &7-5-5x \\\Leftrightarrow & -8x \color{red}{+28} & = &2 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & -8x+5x& = &2-28 \\\Leftrightarrow & -3x& = &-26 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-26}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{26}{3} & & \\ & V = \left\{ \frac{26}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-6)& = & 4 \color{red}{+} (-12+x) \\\Leftrightarrow & -8x-24& = &4-12+x \\\Leftrightarrow & -8x \color{red}{-24} & = &-8 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -8x-x& = &-8+24 \\\Leftrightarrow & -9x& = &16 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{16}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x-5)& = & 4 \color{red}{+} (-9-2x) \\\Leftrightarrow & 3x-15& = &4-9-2x \\\Leftrightarrow & 3x \color{red}{-15} & = &-5 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 3x+2x& = &-5+15 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x+1)& = & -7 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+2& = &-7-14-x \\\Leftrightarrow & 12x \color{red}{+2} & = &-21 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 12x+x& = &-21-2 \\\Leftrightarrow & 13x& = &-23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x+7)& = & 5 \color{red}{+} (-5+x) \\\Leftrightarrow & 12x+28& = &5-5+x \\\Leftrightarrow & 12x \color{red}{+28} & = &0 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 12x-x& = &0-28 \\\Leftrightarrow & 11x& = &-28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x-3)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & -6x-6& = &6-7+x \\\Leftrightarrow & -6x \color{red}{-6} & = &-1 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &-1+6 \\\Leftrightarrow & -7x& = &5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x+3)& = & 10 \color{red}{+} (-2+3x) \\\Leftrightarrow & -10x+15& = &10-2+3x \\\Leftrightarrow & -10x \color{red}{+15} & = &8 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & -10x-3x& = &8-15 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x-2)& = & 15 \color{red}{+} (-11-2x) \\\Leftrightarrow & 15x-6& = &15-11-2x \\\Leftrightarrow & 15x \color{red}{-6} & = &4 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & 15x+2x& = &4+6 \\\Leftrightarrow & 17x& = &10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (5x-5)& = & -12 \color{red}{+} (3-3x) \\\Leftrightarrow & 10x-10& = &-12+3-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &-9 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &-9+10 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)