Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x+6)& = & 15 \color{red}{+} (-11-5x) \\\Leftrightarrow & -6x+12& = &15-11-5x \\\Leftrightarrow & -6x \color{red}{+12} & = &4 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -6x+5x& = &4-12 \\\Leftrightarrow & -x& = &-8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-8}{ \color{red}{-1} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x-1)& = & -3 \color{red}{+} (-13+x) \\\Leftrightarrow & -12x-4& = &-3-13+x \\\Leftrightarrow & -12x \color{red}{-4} & = &-16 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &-16+4 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (2x-6)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x-36& = &6-7+x \\\Leftrightarrow & 12x \color{red}{-36} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 12x-x& = &-1+36 \\\Leftrightarrow & 11x& = &35 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{35}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{35}{11} & & \\ & V = \left\{ \frac{35}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x+6)& = & -14 \color{red}{+} (-6+3x) \\\Leftrightarrow & 10x+30& = &-14-6+3x \\\Leftrightarrow & 10x \color{red}{+30} & = &-20 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &-20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & 10x-3x& = &-20-30 \\\Leftrightarrow & 7x& = &-50 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-50}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-50}{7} & & \\ & V = \left\{ \frac{-50}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x-3)& = & 3 \color{red}{+} (7+x) \\\Leftrightarrow & 24x-18& = &3+7+x \\\Leftrightarrow & 24x \color{red}{-18} & = &10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 24x-x& = &10+18 \\\Leftrightarrow & 23x& = &28 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{28}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{28}{23} & & \\ & V = \left\{ \frac{28}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x-1)& = & 5 \color{red}{-} (-12-5x) \\\Leftrightarrow & -18x-6& = &5+12+5x \\\Leftrightarrow & -18x \color{red}{-6} & = &17 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -18x-5x& = &17+6 \\\Leftrightarrow & -23x& = &23 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{23}{ \color{red}{-23} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-2x-6)& = & 8 \color{red}{+} (13+x) \\\Leftrightarrow & -10x-30& = &8+13+x \\\Leftrightarrow & -10x \color{red}{-30} & = &21 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -10x-x& = &21+30 \\\Leftrightarrow & -11x& = &51 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{51}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-51}{11} & & \\ & V = \left\{ \frac{-51}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+7)& = & -15 \color{red}{-} (1+x) \\\Leftrightarrow & -12x+21& = &-15-1-x \\\Leftrightarrow & -12x \color{red}{+21} & = &-16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -12x+x& = &-16-21 \\\Leftrightarrow & -11x& = &-37 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-37}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{37}{11} & & \\ & V = \left\{ \frac{37}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x+4)& = & -1 \color{red}{+} (-12+x) \\\Leftrightarrow & 4x+16& = &-1-12+x \\\Leftrightarrow & 4x \color{red}{+16} & = &-13 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 4x-x& = &-13-16 \\\Leftrightarrow & 3x& = &-29 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-29}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-29}{3} & & \\ & V = \left\{ \frac{-29}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-5x+2)& = & 14 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x+12& = &14+12-x \\\Leftrightarrow & -30x \color{red}{+12} & = &26 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -30x+x& = &26-12 \\\Leftrightarrow & -29x& = &14 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{14}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-14}{29} & & \\ & V = \left\{ \frac{-14}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x-1)& = & 3 \color{red}{+} (-9+x) \\\Leftrightarrow & 2x-2& = &3-9+x \\\Leftrightarrow & 2x \color{red}{-2} & = &-6 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 2x-x& = &-6+2 \\\Leftrightarrow & x& = &-4 \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x-4)& = & -4 \color{red}{+} (8+x) \\\Leftrightarrow & -12x-24& = &-4+8+x \\\Leftrightarrow & -12x \color{red}{-24} & = &4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -12x-x& = &4+24 \\\Leftrightarrow & -13x& = &28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)