Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-2)& = & -12 \color{red}{-} (-15+3x) \\\Leftrightarrow & -2x-4& = &-12+15-3x \\\Leftrightarrow & -2x \color{red}{-4} & = &3 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -2x+3x& = &3+4 \\\Leftrightarrow & x& = &7 \\ & V = \left\{ 7 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x-1)& = & 14 \color{red}{-} (3-3x) \\\Leftrightarrow & 4x-4& = &14-3+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &11 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &11+4 \\\Leftrightarrow & x& = &15 \\ & V = \left\{ 15 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x+3)& = & -10 \color{red}{-} (10-5x) \\\Leftrightarrow & 18x+18& = &-10-10+5x \\\Leftrightarrow & 18x \color{red}{+18} & = &-20 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 18x-5x& = &-20-18 \\\Leftrightarrow & 13x& = &-38 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-38}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-38}{13} & & \\ & V = \left\{ \frac{-38}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x-7)& = & 9 \color{red}{-} (-4+x) \\\Leftrightarrow & -24x-28& = &9+4-x \\\Leftrightarrow & -24x \color{red}{-28} & = &13 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -24x+x& = &13+28 \\\Leftrightarrow & -23x& = &41 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{41}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-41}{23} & & \\ & V = \left\{ \frac{-41}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-5)& = & -2 \color{red}{-} (2-5x) \\\Leftrightarrow & -18x-15& = &-2-2+5x \\\Leftrightarrow & -18x \color{red}{-15} & = &-4 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+15} \\\Leftrightarrow & -18x-5x& = &-4+15 \\\Leftrightarrow & -23x& = &11 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{11}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x-2)& = & -9 \color{red}{+} (6+4x) \\\Leftrightarrow & -15x-10& = &-9+6+4x \\\Leftrightarrow & -15x \color{red}{-10} & = &-3 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &-3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -15x-4x& = &-3+10 \\\Leftrightarrow & -19x& = &7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-7}{19} & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-3)& = & 5 \color{red}{+} (-9+x) \\\Leftrightarrow & 20x-15& = &5-9+x \\\Leftrightarrow & 20x \color{red}{-15} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 20x-x& = &-4+15 \\\Leftrightarrow & 19x& = &11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x+6)& = & -12 \color{red}{-} (6+x) \\\Leftrightarrow & -2x+12& = &-12-6-x \\\Leftrightarrow & -2x \color{red}{+12} & = &-18 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -2x+x& = &-18-12 \\\Leftrightarrow & -x& = &-30 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-30}{ \color{red}{-1} } \\\Leftrightarrow & x = 30 & & \\ & V = \left\{ 30 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-4)& = & 9 \color{red}{+} (-14-5x) \\\Leftrightarrow & 18x-24& = &9-14-5x \\\Leftrightarrow & 18x \color{red}{-24} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 18x+5x& = &-5+24 \\\Leftrightarrow & 23x& = &19 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{19}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-6)& = & -5 \color{red}{+} (10-3x) \\\Leftrightarrow & 4x-24& = &-5+10-3x \\\Leftrightarrow & 4x \color{red}{-24} & = &5 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 4x+3x& = &5+24 \\\Leftrightarrow & 7x& = &29 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{29}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-6)& = & -6 \color{red}{+} (15+x) \\\Leftrightarrow & -6x-36& = &-6+15+x \\\Leftrightarrow & -6x \color{red}{-36} & = &9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -6x-x& = &9+36 \\\Leftrightarrow & -7x& = &45 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{45}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-45}{7} & & \\ & V = \left\{ \frac{-45}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x-7)& = & -3 \color{red}{-} (14+x) \\\Leftrightarrow & 6x-14& = &-3-14-x \\\Leftrightarrow & 6x \color{red}{-14} & = &-17 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 6x+x& = &-17+14 \\\Leftrightarrow & 7x& = &-3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)