Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+6)& = & 14 \color{red}{-} (12+x) \\\Leftrightarrow & -12x+12& = &14-12-x \\\Leftrightarrow & -12x \color{red}{+12} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &2-12 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x-3)& = & 10 \color{red}{+} (-4-5x) \\\Leftrightarrow & 6x-6& = &10-4-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &6 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &6+6 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x+3)& = & 6 \color{red}{+} (-13-3x) \\\Leftrightarrow & 4x+12& = &6-13-3x \\\Leftrightarrow & 4x \color{red}{+12} & = &-7 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 4x+3x& = &-7-12 \\\Leftrightarrow & 7x& = &-19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x-3)& = & 2 \color{red}{+} (-12+x) \\\Leftrightarrow & 12x-12& = &2-12+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-10+12 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x-4)& = & 11 \color{red}{+} (14+x) \\\Leftrightarrow & 12x-24& = &11+14+x \\\Leftrightarrow & 12x \color{red}{-24} & = &25 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &25+24 \\\Leftrightarrow & 11x& = &49 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{49}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{49}{11} & & \\ & V = \left\{ \frac{49}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x+4)& = & 8 \color{red}{+} (14+4x) \\\Leftrightarrow & -9x+12& = &8+14+4x \\\Leftrightarrow & -9x \color{red}{+12} & = &22 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &22 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & -9x-4x& = &22-12 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-1)& = & 4 \color{red}{-} (15-5x) \\\Leftrightarrow & 8x-4& = &4-15+5x \\\Leftrightarrow & 8x \color{red}{-4} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 8x-5x& = &-11+4 \\\Leftrightarrow & 3x& = &-7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (3x-1)& = & 11 \color{red}{-} (-5+x) \\\Leftrightarrow & 18x-6& = &11+5-x \\\Leftrightarrow & 18x \color{red}{-6} & = &16 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 18x+x& = &16+6 \\\Leftrightarrow & 19x& = &22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{22}{19} & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x-2)& = & 7 \color{red}{+} (1-5x) \\\Leftrightarrow & -6x-6& = &7+1-5x \\\Leftrightarrow & -6x \color{red}{-6} & = &8 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -6x+5x& = &8+6 \\\Leftrightarrow & -x& = &14 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{14}{ \color{red}{-1} } \\\Leftrightarrow & x = -14 & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x-2)& = & 4 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-12& = &4-11-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-7+12 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x-6)& = & -12 \color{red}{+} (5+x) \\\Leftrightarrow & 18x-36& = &-12+5+x \\\Leftrightarrow & 18x \color{red}{-36} & = &-7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 18x-x& = &-7+36 \\\Leftrightarrow & 17x& = &29 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{29}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{29}{17} & & \\ & V = \left\{ \frac{29}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x-3)& = & -1 \color{red}{+} (3-5x) \\\Leftrightarrow & 18x-18& = &-1+3-5x \\\Leftrightarrow & 18x \color{red}{-18} & = &2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 18x+5x& = &2+18 \\\Leftrightarrow & 23x& = &20 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{20}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{20}{23} & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)