Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (2x-1)& = & 12 \color{red}{+} (6-3x) \\\Leftrightarrow & 10x-5& = &12+6-3x \\\Leftrightarrow & 10x \color{red}{-5} & = &18 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 10x+3x& = &18+5 \\\Leftrightarrow & 13x& = &23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x+7)& = & 4 \color{red}{+} (-2+x) \\\Leftrightarrow & -30x+35& = &4-2+x \\\Leftrightarrow & -30x \color{red}{+35} & = &2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -30x-x& = &2-35 \\\Leftrightarrow & -31x& = &-33 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-33}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{33}{31} & & \\ & V = \left\{ \frac{33}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x+1)& = & 12 \color{red}{+} (7+x) \\\Leftrightarrow & 8x+4& = &12+7+x \\\Leftrightarrow & 8x \color{red}{+4} & = &19 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 8x-x& = &19-4 \\\Leftrightarrow & 7x& = &15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x-1)& = & 1 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x-4& = &1+15-x \\\Leftrightarrow & -12x \color{red}{-4} & = &16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &16+4 \\\Leftrightarrow & -11x& = &20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x+4)& = & -7 \color{red}{-} (6-4x) \\\Leftrightarrow & 25x+20& = &-7-6+4x \\\Leftrightarrow & 25x \color{red}{+20} & = &-13 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &-13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & 25x-4x& = &-13-20 \\\Leftrightarrow & 21x& = &-33 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-33}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+7)& = & 1 \color{red}{-} (-4+x) \\\Leftrightarrow & -3x+21& = &1+4-x \\\Leftrightarrow & -3x \color{red}{+21} & = &5 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -3x+x& = &5-21 \\\Leftrightarrow & -2x& = &-16 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-16}{ \color{red}{-2} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+6)& = & 1 \color{red}{+} (11+x) \\\Leftrightarrow & -12x+36& = &1+11+x \\\Leftrightarrow & -12x \color{red}{+36} & = &12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -12x-x& = &12-36 \\\Leftrightarrow & -13x& = &-24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x+2)& = & 10 \color{red}{-} (6+x) \\\Leftrightarrow & -6x+6& = &10-6-x \\\Leftrightarrow & -6x \color{red}{+6} & = &4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -6x+x& = &4-6 \\\Leftrightarrow & -5x& = &-2 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-2}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+3)& = & 14 \color{red}{-} (-3-5x) \\\Leftrightarrow & 18x+18& = &14+3+5x \\\Leftrightarrow & 18x \color{red}{+18} & = &17 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 18x-5x& = &17-18 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x+1)& = & -10 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+6& = &-10+4+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-6-6 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x+1)& = & -9 \color{red}{-} (2+3x) \\\Leftrightarrow & 8x+2& = &-9-2-3x \\\Leftrightarrow & 8x \color{red}{+2} & = &-11 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 8x+3x& = &-11-2 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+6)& = & -7 \color{red}{+} (9-4x) \\\Leftrightarrow & 25x+30& = &-7+9-4x \\\Leftrightarrow & 25x \color{red}{+30} & = &2 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 25x+4x& = &2-30 \\\Leftrightarrow & 29x& = &-28 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-28}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)