Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x-5)& = & 2 \color{red}{-} (-9+x) \\\Leftrightarrow & -5x-25& = &2+9-x \\\Leftrightarrow & -5x \color{red}{-25} & = &11 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -5x+x& = &11+25 \\\Leftrightarrow & -4x& = &36 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{36}{ \color{red}{-4} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x+1)& = & -11 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x+4& = &-11-2+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-13-4 \\\Leftrightarrow & 11x& = &-17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x+7)& = & -14 \color{red}{+} (-5+x) \\\Leftrightarrow & 10x+35& = &-14-5+x \\\Leftrightarrow & 10x \color{red}{+35} & = &-19 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 10x-x& = &-19-35 \\\Leftrightarrow & 9x& = &-54 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-54}{ \color{red}{9} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x-7)& = & 1 \color{red}{-} (1+x) \\\Leftrightarrow & 18x-42& = &1-1-x \\\Leftrightarrow & 18x \color{red}{-42} & = &0 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 18x+x& = &0+42 \\\Leftrightarrow & 19x& = &42 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{42}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{42}{19} & & \\ & V = \left\{ \frac{42}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x+6)& = & -11 \color{red}{+} (-12+2x) \\\Leftrightarrow & 25x+30& = &-11-12+2x \\\Leftrightarrow & 25x \color{red}{+30} & = &-23 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &-23 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & 25x-2x& = &-23-30 \\\Leftrightarrow & 23x& = &-53 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-53}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-53}{23} & & \\ & V = \left\{ \frac{-53}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x+2)& = & 13 \color{red}{-} (-12+x) \\\Leftrightarrow & -9x+6& = &13+12-x \\\Leftrightarrow & -9x \color{red}{+6} & = &25 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -9x+x& = &25-6 \\\Leftrightarrow & -8x& = &19 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{19}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-19}{8} & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-2)& = & -4 \color{red}{+} (-1-2x) \\\Leftrightarrow & -9x-6& = &-4-1-2x \\\Leftrightarrow & -9x \color{red}{-6} & = &-5 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & -9x+2x& = &-5+6 \\\Leftrightarrow & -7x& = &1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x+4)& = & -9 \color{red}{-} (-2-5x) \\\Leftrightarrow & -18x+12& = &-9+2+5x \\\Leftrightarrow & -18x \color{red}{+12} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -18x-5x& = &-7-12 \\\Leftrightarrow & -23x& = &-19 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-19}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x-2)& = & -7 \color{red}{-} (1+x) \\\Leftrightarrow & -12x-6& = &-7-1-x \\\Leftrightarrow & -12x \color{red}{-6} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &-8+6 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x-4)& = & 14 \color{red}{-} (9+x) \\\Leftrightarrow & -12x-8& = &14-9-x \\\Leftrightarrow & -12x \color{red}{-8} & = &5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -12x+x& = &5+8 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x+2)& = & -2 \color{red}{-} (11+x) \\\Leftrightarrow & 24x+8& = &-2-11-x \\\Leftrightarrow & 24x \color{red}{+8} & = &-13 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 24x+x& = &-13-8 \\\Leftrightarrow & 25x& = &-21 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-21}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-21}{25} & & \\ & V = \left\{ \frac{-21}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+6)& = & 12 \color{red}{-} (-4+x) \\\Leftrightarrow & 30x+30& = &12+4-x \\\Leftrightarrow & 30x \color{red}{+30} & = &16 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &16-30 \\\Leftrightarrow & 31x& = &-14 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-14}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)