Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x+2)& = & -1 \color{red}{-} (-11+x) \\\Leftrightarrow & 24x+8& = &-1+11-x \\\Leftrightarrow & 24x \color{red}{+8} & = &10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 24x+x& = &10-8 \\\Leftrightarrow & 25x& = &2 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{2}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{2}{25} & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x-1)& = & -3 \color{red}{+} (5+x) \\\Leftrightarrow & -30x-5& = &-3+5+x \\\Leftrightarrow & -30x \color{red}{-5} & = &2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -30x-x& = &2+5 \\\Leftrightarrow & -31x& = &7 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{7}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-7}{31} & & \\ & V = \left\{ \frac{-7}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x+5)& = & -12 \color{red}{+} (15+x) \\\Leftrightarrow & 6x+10& = &-12+15+x \\\Leftrightarrow & 6x \color{red}{+10} & = &3 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 6x-x& = &3-10 \\\Leftrightarrow & 5x& = &-7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+1)& = & 10 \color{red}{-} (6+x) \\\Leftrightarrow & -6x+3& = &10-6-x \\\Leftrightarrow & -6x \color{red}{+3} & = &4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -6x+x& = &4-3 \\\Leftrightarrow & -5x& = &1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x-7)& = & 14 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x-14& = &14+11-x \\\Leftrightarrow & 12x \color{red}{-14} & = &25 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &25+14 \\\Leftrightarrow & 13x& = &39 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{39}{ \color{red}{13} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x+3)& = & -14 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x+6& = &-14+11-x \\\Leftrightarrow & 12x \color{red}{+6} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &-3-6 \\\Leftrightarrow & 13x& = &-9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x-3)& = & -14 \color{red}{-} (-3+4x) \\\Leftrightarrow & 25x-15& = &-14+3-4x \\\Leftrightarrow & 25x \color{red}{-15} & = &-11 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 25x+4x& = &-11+15 \\\Leftrightarrow & 29x& = &4 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{4}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{4}{29} & & \\ & V = \left\{ \frac{4}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x-2)& = & 14 \color{red}{-} (4+x) \\\Leftrightarrow & 30x-10& = &14-4-x \\\Leftrightarrow & 30x \color{red}{-10} & = &10 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &10+10 \\\Leftrightarrow & 31x& = &20 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{20}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{20}{31} & & \\ & V = \left\{ \frac{20}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-6)& = & -13 \color{red}{-} (-2-5x) \\\Leftrightarrow & 18x-36& = &-13+2+5x \\\Leftrightarrow & 18x \color{red}{-36} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & 18x-5x& = &-11+36 \\\Leftrightarrow & 13x& = &25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+1)& = & 14 \color{red}{-} (-6+x) \\\Leftrightarrow & 30x+5& = &14+6-x \\\Leftrightarrow & 30x \color{red}{+5} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 30x+x& = &20-5 \\\Leftrightarrow & 31x& = &15 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{15}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{15}{31} & & \\ & V = \left\{ \frac{15}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x+4)& = & -15 \color{red}{+} (-11+x) \\\Leftrightarrow & -20x+20& = &-15-11+x \\\Leftrightarrow & -20x \color{red}{+20} & = &-26 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &-26-20 \\\Leftrightarrow & -21x& = &-46 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-46}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{46}{21} & & \\ & V = \left\{ \frac{46}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+4)& = & 1 \color{red}{-} (-7+2x) \\\Leftrightarrow & 9x+12& = &1+7-2x \\\Leftrightarrow & 9x \color{red}{+12} & = &8 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & 9x+2x& = &8-12 \\\Leftrightarrow & 11x& = &-4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)