Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x+1)& = & -15 \color{red}{+} (14+x) \\\Leftrightarrow & 12x+6& = &-15+14+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-1-6 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x+7)& = & -10 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x+42& = &-10-6+x \\\Leftrightarrow & 24x \color{red}{+42} & = &-16 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 24x-x& = &-16-42 \\\Leftrightarrow & 23x& = &-58 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-58}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-58}{23} & & \\ & V = \left\{ \frac{-58}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x-7)& = & -5 \color{red}{+} (-4+x) \\\Leftrightarrow & 20x-28& = &-5-4+x \\\Leftrightarrow & 20x \color{red}{-28} & = &-9 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 20x-x& = &-9+28 \\\Leftrightarrow & 19x& = &19 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{19}{ \color{red}{19} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x+4)& = & 14 \color{red}{-} (9-5x) \\\Leftrightarrow & 6x+24& = &14-9+5x \\\Leftrightarrow & 6x \color{red}{+24} & = &5 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 6x-5x& = &5-24 \\\Leftrightarrow & x& = &-19 \\ & V = \left\{ -19 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-5x-1)& = & 10 \color{red}{+} (5+x) \\\Leftrightarrow & -30x-6& = &10+5+x \\\Leftrightarrow & -30x \color{red}{-6} & = &15 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -30x-x& = &15+6 \\\Leftrightarrow & -31x& = &21 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{21}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-21}{31} & & \\ & V = \left\{ \frac{-21}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x+7)& = & 3 \color{red}{+} (-15-5x) \\\Leftrightarrow & -6x+21& = &3-15-5x \\\Leftrightarrow & -6x \color{red}{+21} & = &-12 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & -6x+5x& = &-12-21 \\\Leftrightarrow & -x& = &-33 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-33}{ \color{red}{-1} } \\\Leftrightarrow & x = 33 & & \\ & V = \left\{ 33 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x-6)& = & 12 \color{red}{-} (14+x) \\\Leftrightarrow & 12x-24& = &12-14-x \\\Leftrightarrow & 12x \color{red}{-24} & = &-2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &-2+24 \\\Leftrightarrow & 13x& = &22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x-5)& = & -13 \color{red}{+} (-11+x) \\\Leftrightarrow & -20x-25& = &-13-11+x \\\Leftrightarrow & -20x \color{red}{-25} & = &-24 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -20x-x& = &-24+25 \\\Leftrightarrow & -21x& = &1 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{1}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x+6)& = & -11 \color{red}{+} (-5-5x) \\\Leftrightarrow & -8x+12& = &-11-5-5x \\\Leftrightarrow & -8x \color{red}{+12} & = &-16 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -8x+5x& = &-16-12 \\\Leftrightarrow & -3x& = &-28 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-28}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{28}{3} & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-7)& = & 8 \color{red}{-} (-5-3x) \\\Leftrightarrow & -4x-28& = &8+5+3x \\\Leftrightarrow & -4x \color{red}{-28} & = &13 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -4x-3x& = &13+28 \\\Leftrightarrow & -7x& = &41 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{41}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-41}{7} & & \\ & V = \left\{ \frac{-41}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x-7)& = & 4 \color{red}{+} (5+x) \\\Leftrightarrow & 24x-42& = &4+5+x \\\Leftrightarrow & 24x \color{red}{-42} & = &9 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 24x-x& = &9+42 \\\Leftrightarrow & 23x& = &51 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{51}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{51}{23} & & \\ & V = \left\{ \frac{51}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x-2)& = & -12 \color{red}{+} (5+x) \\\Leftrightarrow & -2x-4& = &-12+5+x \\\Leftrightarrow & -2x \color{red}{-4} & = &-7 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -2x-x& = &-7+4 \\\Leftrightarrow & -3x& = &-3 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-3}{ \color{red}{-3} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)