Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x-4)& = & -2 \color{red}{+} (8+x) \\\Leftrightarrow & -6x-8& = &-2+8+x \\\Leftrightarrow & -6x \color{red}{-8} & = &6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -6x-x& = &6+8 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+4)& = & 8 \color{red}{+} (4+x) \\\Leftrightarrow & 2x+8& = &8+4+x \\\Leftrightarrow & 2x \color{red}{+8} & = &12 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 2x-x& = &12-8 \\\Leftrightarrow & x& = &4 \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+6)& = & 1 \color{red}{+} (2+3x) \\\Leftrightarrow & -20x+24& = &1+2+3x \\\Leftrightarrow & -20x \color{red}{+24} & = &3 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -20x-3x& = &3-24 \\\Leftrightarrow & -23x& = &-21 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-21}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x-2)& = & -5 \color{red}{+} (-5-2x) \\\Leftrightarrow & -15x-6& = &-5-5-2x \\\Leftrightarrow & -15x \color{red}{-6} & = &-10 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &-10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & -15x+2x& = &-10+6 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-7)& = & -6 \color{red}{+} (6+x) \\\Leftrightarrow & 12x-28& = &-6+6+x \\\Leftrightarrow & 12x \color{red}{-28} & = &0 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 12x-x& = &0+28 \\\Leftrightarrow & 11x& = &28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-1)& = & -9 \color{red}{-} (-12+x) \\\Leftrightarrow & 24x-4& = &-9+12-x \\\Leftrightarrow & 24x \color{red}{-4} & = &3 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &3+4 \\\Leftrightarrow & 25x& = &7 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{7}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{7}{25} & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x+1)& = & -6 \color{red}{+} (11-3x) \\\Leftrightarrow & -10x+2& = &-6+11-3x \\\Leftrightarrow & -10x \color{red}{+2} & = &5 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -10x+3x& = &5-2 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x-2)& = & -1 \color{red}{-} (-11-2x) \\\Leftrightarrow & 5x-10& = &-1+11+2x \\\Leftrightarrow & 5x \color{red}{-10} & = &10 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+10} \\\Leftrightarrow & 5x-2x& = &10+10 \\\Leftrightarrow & 3x& = &20 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{20}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{20}{3} & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x+3)& = & -10 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x+18& = &-10-4+x \\\Leftrightarrow & -12x \color{red}{+18} & = &-14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &-14-18 \\\Leftrightarrow & -13x& = &-32 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-32}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x+4)& = & 6 \color{red}{+} (6+x) \\\Leftrightarrow & 6x+24& = &6+6+x \\\Leftrightarrow & 6x \color{red}{+24} & = &12 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 6x-x& = &12-24 \\\Leftrightarrow & 5x& = &-12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x+3)& = & -8 \color{red}{-} (10+x) \\\Leftrightarrow & -15x+9& = &-8-10-x \\\Leftrightarrow & -15x \color{red}{+9} & = &-18 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -15x+x& = &-18-9 \\\Leftrightarrow & -14x& = &-27 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-27}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{27}{14} & & \\ & V = \left\{ \frac{27}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x+3)& = & 13 \color{red}{-} (4+x) \\\Leftrightarrow & 8x+12& = &13-4-x \\\Leftrightarrow & 8x \color{red}{+12} & = &9 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 8x+x& = &9-12 \\\Leftrightarrow & 9x& = &-3 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-3}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)