Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-3x+6)=15+(1+x)\)
2. \(6(3x+4)=9+(-13+5x)\)
3. \(2(4x+5)=-8+(-1+3x)\)
4. \(3(-3x+2)=11+(-13+2x)\)
5. \(5(4x+2)=7+(-1+3x)\)
6. \(6(-5x-6)=14+(-1+x)\)
7. \(5(-6x-4)=12-(-1+29x)\)
8. \(3(5x-4)=-14+(9+4x)\)
9. \(3(3x-6)=5-(9-4x)\)
10. \(6(4x+5)=-5-(7+5x)\)
11. \(6(-3x+1)=14-(-6+5x)\)
12. \(6(x-4)=1-(-11+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+6)& = & 15 \color{red}{+} (1+x) \\\Leftrightarrow & -9x+18& = &15+1+x \\\Leftrightarrow & -9x \color{red}{+18} & = &16 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -9x-x& = &16-18 \\\Leftrightarrow & -10x& = &-2 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-2}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x+4)& = & 9 \color{red}{+} (-13+5x) \\\Leftrightarrow & 18x+24& = &9-13+5x \\\Leftrightarrow & 18x \color{red}{+24} & = &-4 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 18x-5x& = &-4-24 \\\Leftrightarrow & 13x& = &-28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+5)& = & -8 \color{red}{+} (-1+3x) \\\Leftrightarrow & 8x+10& = &-8-1+3x \\\Leftrightarrow & 8x \color{red}{+10} & = &-9 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 8x-3x& = &-9-10 \\\Leftrightarrow & 5x& = &-19 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-19}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-19}{5} & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x+2)& = & 11 \color{red}{+} (-13+2x) \\\Leftrightarrow & -9x+6& = &11-13+2x \\\Leftrightarrow & -9x \color{red}{+6} & = &-2 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & -9x-2x& = &-2-6 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x+2)& = & 7 \color{red}{+} (-1+3x) \\\Leftrightarrow & 20x+10& = &7-1+3x \\\Leftrightarrow & 20x \color{red}{+10} & = &6 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 20x-3x& = &6-10 \\\Leftrightarrow & 17x& = &-4 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-4}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x-6)& = & 14 \color{red}{+} (-1+x) \\\Leftrightarrow & -30x-36& = &14-1+x \\\Leftrightarrow & -30x \color{red}{-36} & = &13 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -30x-x& = &13+36 \\\Leftrightarrow & -31x& = &49 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{49}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-49}{31} & & \\ & V = \left\{ \frac{-49}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-4)& = & 12 \color{red}{-} (-1+29x) \\\Leftrightarrow & -30x-20& = &12+1-29x \\\Leftrightarrow & -30x \color{red}{-20} & = &13 \color{red}{-29x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+29x} & = &13 \color{red}{-29x} \color{blue}{+29x} \color{blue}{+20} \\\Leftrightarrow & -30x+29x& = &13+20 \\\Leftrightarrow & -x& = &33 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{33}{ \color{red}{-1} } \\\Leftrightarrow & x = -33 & & \\ & V = \left\{ -33 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x-4)& = & -14 \color{red}{+} (9+4x) \\\Leftrightarrow & 15x-12& = &-14+9+4x \\\Leftrightarrow & 15x \color{red}{-12} & = &-5 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{-4x} & = &-5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+12} \\\Leftrightarrow & 15x-4x& = &-5+12 \\\Leftrightarrow & 11x& = &7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-6)& = & 5 \color{red}{-} (9-4x) \\\Leftrightarrow & 9x-18& = &5-9+4x \\\Leftrightarrow & 9x \color{red}{-18} & = &-4 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{-4x} & = &-4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+18} \\\Leftrightarrow & 9x-4x& = &-4+18 \\\Leftrightarrow & 5x& = &14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x+5)& = & -5 \color{red}{-} (7+5x) \\\Leftrightarrow & 24x+30& = &-5-7-5x \\\Leftrightarrow & 24x \color{red}{+30} & = &-12 \color{red}{-5x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & 24x+5x& = &-12-30 \\\Leftrightarrow & 29x& = &-42 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-42}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-42}{29} & & \\ & V = \left\{ \frac{-42}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x+1)& = & 14 \color{red}{-} (-6+5x) \\\Leftrightarrow & -18x+6& = &14+6-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &20 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &20-6 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x-4)& = & 1 \color{red}{-} (-11+x) \\\Leftrightarrow & 6x-24& = &1+11-x \\\Leftrightarrow & 6x \color{red}{-24} & = &12 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 6x+x& = &12+24 \\\Leftrightarrow & 7x& = &36 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{36}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{36}{7} & & \\ & V = \left\{ \frac{36}{7} \right\} & \\\end{align}\)