Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x-4)& = & -2 \color{red}{-} (8-4x) \\\Leftrightarrow & 9x-12& = &-2-8+4x \\\Leftrightarrow & 9x \color{red}{-12} & = &-10 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{-4x} & = &-10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+12} \\\Leftrightarrow & 9x-4x& = &-10+12 \\\Leftrightarrow & 5x& = &2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-6)& = & 11 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x-18& = &11+3-x \\\Leftrightarrow & 12x \color{red}{-18} & = &14 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &14+18 \\\Leftrightarrow & 13x& = &32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x+4)& = & 8 \color{red}{-} (6+x) \\\Leftrightarrow & -12x+12& = &8-6-x \\\Leftrightarrow & -12x \color{red}{+12} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &2-12 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+4)& = & 10 \color{red}{-} (7+x) \\\Leftrightarrow & -12x+16& = &10-7-x \\\Leftrightarrow & -12x \color{red}{+16} & = &3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -12x+x& = &3-16 \\\Leftrightarrow & -11x& = &-13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x-1)& = & -10 \color{red}{+} (-13+x) \\\Leftrightarrow & -6x-3& = &-10-13+x \\\Leftrightarrow & -6x \color{red}{-3} & = &-23 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -6x-x& = &-23+3 \\\Leftrightarrow & -7x& = &-20 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-20}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-5)& = & -4 \color{red}{+} (12+2x) \\\Leftrightarrow & -25x-25& = &-4+12+2x \\\Leftrightarrow & -25x \color{red}{-25} & = &8 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & -25x-2x& = &8+25 \\\Leftrightarrow & -27x& = &33 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{33}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{-11}{9} & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x+1)& = & -10 \color{red}{-} (15+x) \\\Leftrightarrow & 12x+3& = &-10-15-x \\\Leftrightarrow & 12x \color{red}{+3} & = &-25 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &-25-3 \\\Leftrightarrow & 13x& = &-28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x-6)& = & -13 \color{red}{+} (-4+x) \\\Leftrightarrow & 9x-18& = &-13-4+x \\\Leftrightarrow & 9x \color{red}{-18} & = &-17 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 9x-x& = &-17+18 \\\Leftrightarrow & 8x& = &1 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{1}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+4)& = & 7 \color{red}{+} (-5+x) \\\Leftrightarrow & -20x+20& = &7-5+x \\\Leftrightarrow & -20x \color{red}{+20} & = &2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &2-20 \\\Leftrightarrow & -21x& = &-18 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-18}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x-5)& = & -3 \color{red}{-} (1-2x) \\\Leftrightarrow & -15x-25& = &-3-1+2x \\\Leftrightarrow & -15x \color{red}{-25} & = &-4 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & -15x-2x& = &-4+25 \\\Leftrightarrow & -17x& = &21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-3)& = & 12 \color{red}{-} (-15-5x) \\\Leftrightarrow & -36x-18& = &12+15+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &27 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &27 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &27+18 \\\Leftrightarrow & -41x& = &45 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{45}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-45}{41} & & \\ & V = \left\{ \frac{-45}{41} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+4)& = & 10 \color{red}{+} (-15+x) \\\Leftrightarrow & -20x+16& = &10-15+x \\\Leftrightarrow & -20x \color{red}{+16} & = &-5 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -20x-x& = &-5-16 \\\Leftrightarrow & -21x& = &-21 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-21}{ \color{red}{-21} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)