Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x-6)& = & -10 \color{red}{+} (3+x) \\\Leftrightarrow & 6x-36& = &-10+3+x \\\Leftrightarrow & 6x \color{red}{-36} & = &-7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 6x-x& = &-7+36 \\\Leftrightarrow & 5x& = &29 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{29}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{29}{5} & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x+5)& = & -14 \color{red}{-} (-9+x) \\\Leftrightarrow & -8x+10& = &-14+9-x \\\Leftrightarrow & -8x \color{red}{+10} & = &-5 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -8x+x& = &-5-10 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x-7)& = & 2 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-28& = &2+4+x \\\Leftrightarrow & 12x \color{red}{-28} & = &6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 12x-x& = &6+28 \\\Leftrightarrow & 11x& = &34 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{34}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{34}{11} & & \\ & V = \left\{ \frac{34}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x-6)& = & -1 \color{red}{+} (15+x) \\\Leftrightarrow & -4x-24& = &-1+15+x \\\Leftrightarrow & -4x \color{red}{-24} & = &14 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -4x-x& = &14+24 \\\Leftrightarrow & -5x& = &38 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{38}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-38}{5} & & \\ & V = \left\{ \frac{-38}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x+6)& = & 13 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x+24& = &13+4-x \\\Leftrightarrow & 12x \color{red}{+24} & = &17 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 12x+x& = &17-24 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+7)& = & -10 \color{red}{+} (-14+x) \\\Leftrightarrow & 24x+42& = &-10-14+x \\\Leftrightarrow & 24x \color{red}{+42} & = &-24 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 24x-x& = &-24-42 \\\Leftrightarrow & 23x& = &-66 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-66}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-66}{23} & & \\ & V = \left\{ \frac{-66}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x-2)& = & -11 \color{red}{+} (-1+x) \\\Leftrightarrow & -30x-12& = &-11-1+x \\\Leftrightarrow & -30x \color{red}{-12} & = &-12 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -30x-x& = &-12+12 \\\Leftrightarrow & -31x& = &0 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{0}{ \color{red}{-31} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x+3)& = & 2 \color{red}{-} (2+x) \\\Leftrightarrow & 6x+9& = &2-2-x \\\Leftrightarrow & 6x \color{red}{+9} & = &0 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 6x+x& = &0-9 \\\Leftrightarrow & 7x& = &-9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-5x+1)& = & 7 \color{red}{-} (10-2x) \\\Leftrightarrow & -15x+3& = &7-10+2x \\\Leftrightarrow & -15x \color{red}{+3} & = &-3 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -15x-2x& = &-3-3 \\\Leftrightarrow & -17x& = &-6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x-7)& = & -5 \color{red}{-} (3+x) \\\Leftrightarrow & -20x-28& = &-5-3-x \\\Leftrightarrow & -20x \color{red}{-28} & = &-8 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -20x+x& = &-8+28 \\\Leftrightarrow & -19x& = &20 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{20}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-20}{19} & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-2x+6)& = & 12 \color{red}{-} (-6+x) \\\Leftrightarrow & -6x+18& = &12+6-x \\\Leftrightarrow & -6x \color{red}{+18} & = &18 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &18-18 \\\Leftrightarrow & -5x& = &0 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{0}{ \color{red}{-5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+6)& = & 14 \color{red}{-} (-7-2x) \\\Leftrightarrow & 9x+18& = &14+7+2x \\\Leftrightarrow & 9x \color{red}{+18} & = &21 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &21 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & 9x-2x& = &21-18 \\\Leftrightarrow & 7x& = &3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)