Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x-3)& = & 7 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x-9& = &7-7+x \\\Leftrightarrow & -12x \color{red}{-9} & = &0 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -12x-x& = &0+9 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-6x+2)& = & -6 \color{red}{-} (13+x) \\\Leftrightarrow & -12x+4& = &-6-13-x \\\Leftrightarrow & -12x \color{red}{+4} & = &-19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &-19-4 \\\Leftrightarrow & -11x& = &-23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x+6)& = & 8 \color{red}{+} (8+x) \\\Leftrightarrow & -2x+12& = &8+8+x \\\Leftrightarrow & -2x \color{red}{+12} & = &16 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -2x-x& = &16-12 \\\Leftrightarrow & -3x& = &4 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{4}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x-5)& = & 1 \color{red}{+} (-10+3x) \\\Leftrightarrow & 10x-25& = &1-10+3x \\\Leftrightarrow & 10x \color{red}{-25} & = &-9 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & 10x-3x& = &-9+25 \\\Leftrightarrow & 7x& = &16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+7)& = & 13 \color{red}{-} (11+x) \\\Leftrightarrow & -24x+28& = &13-11-x \\\Leftrightarrow & -24x \color{red}{+28} & = &2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -24x+x& = &2-28 \\\Leftrightarrow & -23x& = &-26 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-26}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{26}{23} & & \\ & V = \left\{ \frac{26}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x-3)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & 30x-18& = &11-10-x \\\Leftrightarrow & 30x \color{red}{-18} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &1+18 \\\Leftrightarrow & 31x& = &19 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{19}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{19}{31} & & \\ & V = \left\{ \frac{19}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x-3)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & 6x-6& = &6-7+x \\\Leftrightarrow & 6x \color{red}{-6} & = &-1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 6x-x& = &-1+6 \\\Leftrightarrow & 5x& = &5 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{5}{ \color{red}{5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x+1)& = & 11 \color{red}{-} (14+2x) \\\Leftrightarrow & 9x+3& = &11-14-2x \\\Leftrightarrow & 9x \color{red}{+3} & = &-3 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & 9x+2x& = &-3-3 \\\Leftrightarrow & 11x& = &-6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x+3)& = & -10 \color{red}{+} (-7+x) \\\Leftrightarrow & 20x+12& = &-10-7+x \\\Leftrightarrow & 20x \color{red}{+12} & = &-17 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 20x-x& = &-17-12 \\\Leftrightarrow & 19x& = &-29 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-29}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-29}{19} & & \\ & V = \left\{ \frac{-29}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+2)& = & -1 \color{red}{+} (5+2x) \\\Leftrightarrow & -15x+6& = &-1+5+2x \\\Leftrightarrow & -15x \color{red}{+6} & = &4 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & -15x-2x& = &4-6 \\\Leftrightarrow & -17x& = &-2 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-2}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-5)& = & -8 \color{red}{+} (-11+x) \\\Leftrightarrow & -36x-30& = &-8-11+x \\\Leftrightarrow & -36x \color{red}{-30} & = &-19 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -36x-x& = &-19+30 \\\Leftrightarrow & -37x& = &11 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{11}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-11}{37} & & \\ & V = \left\{ \frac{-11}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x+4)& = & -3 \color{red}{-} (15+x) \\\Leftrightarrow & 18x+12& = &-3-15-x \\\Leftrightarrow & 18x \color{red}{+12} & = &-18 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &-18-12 \\\Leftrightarrow & 19x& = &-30 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-30}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-30}{19} & & \\ & V = \left\{ \frac{-30}{19} \right\} & \\\end{align}\)