Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x-1)& = & -9 \color{red}{-} (-11+x) \\\Leftrightarrow & -12x-3& = &-9+11-x \\\Leftrightarrow & -12x \color{red}{-3} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -12x+x& = &2+3 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x-4)& = & -15 \color{red}{+} (-5+x) \\\Leftrightarrow & -30x-24& = &-15-5+x \\\Leftrightarrow & -30x \color{red}{-24} & = &-20 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -30x-x& = &-20+24 \\\Leftrightarrow & -31x& = &4 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{4}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-4}{31} & & \\ & V = \left\{ \frac{-4}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x+1)& = & 9 \color{red}{-} (8+x) \\\Leftrightarrow & -4x+4& = &9-8-x \\\Leftrightarrow & -4x \color{red}{+4} & = &1 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -4x+x& = &1-4 \\\Leftrightarrow & -3x& = &-3 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-3}{ \color{red}{-3} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+2)& = & 14 \color{red}{-} (11+x) \\\Leftrightarrow & -6x+6& = &14-11-x \\\Leftrightarrow & -6x \color{red}{+6} & = &3 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -6x+x& = &3-6 \\\Leftrightarrow & -5x& = &-3 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-3}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x+1)& = & -15 \color{red}{-} (-8+x) \\\Leftrightarrow & -5x+5& = &-15+8-x \\\Leftrightarrow & -5x \color{red}{+5} & = &-7 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -5x+x& = &-7-5 \\\Leftrightarrow & -4x& = &-12 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-12}{ \color{red}{-4} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x-2)& = & -10 \color{red}{-} (2+4x) \\\Leftrightarrow & 15x-6& = &-10-2-4x \\\Leftrightarrow & 15x \color{red}{-6} & = &-12 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & 15x+4x& = &-12+6 \\\Leftrightarrow & 19x& = &-6 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-6}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x-3)& = & -6 \color{red}{-} (11+x) \\\Leftrightarrow & 2x-6& = &-6-11-x \\\Leftrightarrow & 2x \color{red}{-6} & = &-17 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 2x+x& = &-17+6 \\\Leftrightarrow & 3x& = &-11 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-11}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x-5)& = & 14 \color{red}{+} (12+x) \\\Leftrightarrow & 10x-25& = &14+12+x \\\Leftrightarrow & 10x \color{red}{-25} & = &26 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 10x-x& = &26+25 \\\Leftrightarrow & 9x& = &51 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{51}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{17}{3} & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x+5)& = & -12 \color{red}{-} (-10+3x) \\\Leftrightarrow & 4x+20& = &-12+10-3x \\\Leftrightarrow & 4x \color{red}{+20} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 4x+3x& = &-2-20 \\\Leftrightarrow & 7x& = &-22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x+4)& = & 14 \color{red}{+} (10+x) \\\Leftrightarrow & -3x+12& = &14+10+x \\\Leftrightarrow & -3x \color{red}{+12} & = &24 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -3x-x& = &24-12 \\\Leftrightarrow & -4x& = &12 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{12}{ \color{red}{-4} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x-3)& = & -13 \color{red}{-} (15+x) \\\Leftrightarrow & 12x-9& = &-13-15-x \\\Leftrightarrow & 12x \color{red}{-9} & = &-28 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 12x+x& = &-28+9 \\\Leftrightarrow & 13x& = &-19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x-5)& = & 9 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x-15& = &9+12-x \\\Leftrightarrow & -12x \color{red}{-15} & = &21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -12x+x& = &21+15 \\\Leftrightarrow & -11x& = &36 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{36}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-36}{11} & & \\ & V = \left\{ \frac{-36}{11} \right\} & \\\end{align}\)