Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+1)& = & 7 \color{red}{+} (-1+x) \\\Leftrightarrow & 15x+3& = &7-1+x \\\Leftrightarrow & 15x \color{red}{+3} & = &6 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 15x-x& = &6-3 \\\Leftrightarrow & 14x& = &3 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{3}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{3}{14} & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x-4)& = & -8 \color{red}{-} (15-5x) \\\Leftrightarrow & -18x-12& = &-8-15+5x \\\Leftrightarrow & -18x \color{red}{-12} & = &-23 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-23 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -18x-5x& = &-23+12 \\\Leftrightarrow & -23x& = &-11 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-11}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x+5)& = & -3 \color{red}{+} (13-2x) \\\Leftrightarrow & 9x+15& = &-3+13-2x \\\Leftrightarrow & 9x \color{red}{+15} & = &10 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 9x+2x& = &10-15 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-4)& = & 11 \color{red}{-} (-1-5x) \\\Leftrightarrow & -6x-24& = &11+1+5x \\\Leftrightarrow & -6x \color{red}{-24} & = &12 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & -6x-5x& = &12+24 \\\Leftrightarrow & -11x& = &36 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{36}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-36}{11} & & \\ & V = \left\{ \frac{-36}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x+4)& = & -13 \color{red}{+} (-11+x) \\\Leftrightarrow & 24x+16& = &-13-11+x \\\Leftrightarrow & 24x \color{red}{+16} & = &-24 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 24x-x& = &-24-16 \\\Leftrightarrow & 23x& = &-40 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-40}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-40}{23} & & \\ & V = \left\{ \frac{-40}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x+3)& = & 2 \color{red}{-} (-5+3x) \\\Leftrightarrow & 10x+6& = &2+5-3x \\\Leftrightarrow & 10x \color{red}{+6} & = &7 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 10x+3x& = &7-6 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-7)& = & 13 \color{red}{+} (-10-4x) \\\Leftrightarrow & -9x-21& = &13-10-4x \\\Leftrightarrow & -9x \color{red}{-21} & = &3 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & -9x+4x& = &3+21 \\\Leftrightarrow & -5x& = &24 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{24}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-24}{5} & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x+2)& = & 13 \color{red}{-} (15+x) \\\Leftrightarrow & 12x+4& = &13-15-x \\\Leftrightarrow & 12x \color{red}{+4} & = &-2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &-2-4 \\\Leftrightarrow & 13x& = &-6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x-4)& = & -7 \color{red}{-} (-7-2x) \\\Leftrightarrow & -5x-20& = &-7+7+2x \\\Leftrightarrow & -5x \color{red}{-20} & = &0 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+20} \\\Leftrightarrow & -5x-2x& = &0+20 \\\Leftrightarrow & -7x& = &20 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{20}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x-7)& = & 12 \color{red}{+} (-2+x) \\\Leftrightarrow & -24x-42& = &12-2+x \\\Leftrightarrow & -24x \color{red}{-42} & = &10 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -24x-x& = &10+42 \\\Leftrightarrow & -25x& = &52 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{52}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-52}{25} & & \\ & V = \left\{ \frac{-52}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (2x+2)& = & -6 \color{red}{+} (-6-3x) \\\Leftrightarrow & 10x+10& = &-6-6-3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-12 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 10x+3x& = &-12-10 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (2x-1)& = & -3 \color{red}{+} (3+x) \\\Leftrightarrow & 4x-2& = &-3+3+x \\\Leftrightarrow & 4x \color{red}{-2} & = &0 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 4x-x& = &0+2 \\\Leftrightarrow & 3x& = &2 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{2}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)