Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+4)& = & -14 \color{red}{+} (10+x) \\\Leftrightarrow & -30x+24& = &-14+10+x \\\Leftrightarrow & -30x \color{red}{+24} & = &-4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -30x-x& = &-4-24 \\\Leftrightarrow & -31x& = &-28 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-28}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{28}{31} & & \\ & V = \left\{ \frac{28}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x+1)& = & -2 \color{red}{+} (-11-4x) \\\Leftrightarrow & 9x+3& = &-2-11-4x \\\Leftrightarrow & 9x \color{red}{+3} & = &-13 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &-13 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 9x+4x& = &-13-3 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-x-7)& = & 4 \color{red}{+} (-2-5x) \\\Leftrightarrow & -3x-21& = &4-2-5x \\\Leftrightarrow & -3x \color{red}{-21} & = &2 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & -3x+5x& = &2+21 \\\Leftrightarrow & 2x& = &23 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{23}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{23}{2} & & \\ & V = \left\{ \frac{23}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-2)& = & -11 \color{red}{-} (-10+x) \\\Leftrightarrow & -6x-12& = &-11+10-x \\\Leftrightarrow & -6x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &-1+12 \\\Leftrightarrow & -5x& = &11 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{11}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-11}{5} & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x-5)& = & -15 \color{red}{-} (15-5x) \\\Leftrightarrow & -6x-15& = &-15-15+5x \\\Leftrightarrow & -6x \color{red}{-15} & = &-30 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-5x} & = &-30 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+15} \\\Leftrightarrow & -6x-5x& = &-30+15 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x-2)& = & 14 \color{red}{+} (12-4x) \\\Leftrightarrow & 5x-10& = &14+12-4x \\\Leftrightarrow & 5x \color{red}{-10} & = &26 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &26 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & 5x+4x& = &26+10 \\\Leftrightarrow & 9x& = &36 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{36}{ \color{red}{9} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-2)& = & -13 \color{red}{-} (-3+x) \\\Leftrightarrow & 3x-6& = &-13+3-x \\\Leftrightarrow & 3x \color{red}{-6} & = &-10 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 3x+x& = &-10+6 \\\Leftrightarrow & 4x& = &-4 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-4}{ \color{red}{4} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x-1)& = & 14 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-6& = &14+13-x \\\Leftrightarrow & -12x \color{red}{-6} & = &27 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &27+6 \\\Leftrightarrow & -11x& = &33 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{33}{ \color{red}{-11} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-6)& = & 3 \color{red}{+} (2+x) \\\Leftrightarrow & -12x-12& = &3+2+x \\\Leftrightarrow & -12x \color{red}{-12} & = &5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &5+12 \\\Leftrightarrow & -13x& = &17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x+3)& = & -4 \color{red}{-} (13+x) \\\Leftrightarrow & 24x+12& = &-4-13-x \\\Leftrightarrow & 24x \color{red}{+12} & = &-17 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 24x+x& = &-17-12 \\\Leftrightarrow & 25x& = &-29 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-29}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-29}{25} & & \\ & V = \left\{ \frac{-29}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x+5)& = & -11 \color{red}{+} (7+2x) \\\Leftrightarrow & -3x+15& = &-11+7+2x \\\Leftrightarrow & -3x \color{red}{+15} & = &-4 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -3x-2x& = &-4-15 \\\Leftrightarrow & -5x& = &-19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{19}{5} & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x-4)& = & -13 \color{red}{+} (-5+x) \\\Leftrightarrow & -2x-8& = &-13-5+x \\\Leftrightarrow & -2x \color{red}{-8} & = &-18 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -2x-x& = &-18+8 \\\Leftrightarrow & -3x& = &-10 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-10}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)