Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x+2)& = & 14 \color{red}{-} (-4-4x) \\\Leftrightarrow & -25x+10& = &14+4+4x \\\Leftrightarrow & -25x \color{red}{+10} & = &18 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-4x} & = &18 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-10} \\\Leftrightarrow & -25x-4x& = &18-10 \\\Leftrightarrow & -29x& = &8 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{8}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-8}{29} & & \\ & V = \left\{ \frac{-8}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+4)& = & 8 \color{red}{+} (-3+x) \\\Leftrightarrow & 20x+16& = &8-3+x \\\Leftrightarrow & 20x \color{red}{+16} & = &5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 20x-x& = &5-16 \\\Leftrightarrow & 19x& = &-11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x-5)& = & -6 \color{red}{-} (-12+x) \\\Leftrightarrow & -18x-15& = &-6+12-x \\\Leftrightarrow & -18x \color{red}{-15} & = &6 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -18x+x& = &6+15 \\\Leftrightarrow & -17x& = &21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-6)& = & 7 \color{red}{-} (-11+x) \\\Leftrightarrow & 16x-24& = &7+11-x \\\Leftrightarrow & 16x \color{red}{-24} & = &18 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 16x+x& = &18+24 \\\Leftrightarrow & 17x& = &42 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{42}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{42}{17} & & \\ & V = \left\{ \frac{42}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x+1)& = & -13 \color{red}{-} (1+x) \\\Leftrightarrow & 6x+3& = &-13-1-x \\\Leftrightarrow & 6x \color{red}{+3} & = &-14 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 6x+x& = &-14-3 \\\Leftrightarrow & 7x& = &-17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+1)& = & 11 \color{red}{+} (12+x) \\\Leftrightarrow & 12x+6& = &11+12+x \\\Leftrightarrow & 12x \color{red}{+6} & = &23 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &23-6 \\\Leftrightarrow & 11x& = &17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-3)& = & 1 \color{red}{+} (2-5x) \\\Leftrightarrow & 6x-18& = &1+2-5x \\\Leftrightarrow & 6x \color{red}{-18} & = &3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 6x+5x& = &3+18 \\\Leftrightarrow & 11x& = &21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x+4)& = & 5 \color{red}{-} (-12+x) \\\Leftrightarrow & -3x+12& = &5+12-x \\\Leftrightarrow & -3x \color{red}{+12} & = &17 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -3x+x& = &17-12 \\\Leftrightarrow & -2x& = &5 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{5}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x+3)& = & 6 \color{red}{+} (2-3x) \\\Leftrightarrow & 10x+15& = &6+2-3x \\\Leftrightarrow & 10x \color{red}{+15} & = &8 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+15} \color{blue}{-15} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-15} \\\Leftrightarrow & 10x+3x& = &8-15 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-5)& = & 14 \color{red}{+} (-8+x) \\\Leftrightarrow & -4x-10& = &14-8+x \\\Leftrightarrow & -4x \color{red}{-10} & = &6 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -4x-x& = &6+10 \\\Leftrightarrow & -5x& = &16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-16}{5} & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-4)& = & 13 \color{red}{+} (-8+x) \\\Leftrightarrow & -18x-12& = &13-8+x \\\Leftrightarrow & -18x \color{red}{-12} & = &5 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -18x-x& = &5+12 \\\Leftrightarrow & -19x& = &17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x-2)& = & 3 \color{red}{+} (13-2x) \\\Leftrightarrow & 5x-10& = &3+13-2x \\\Leftrightarrow & 5x \color{red}{-10} & = &16 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & 5x+2x& = &16+10 \\\Leftrightarrow & 7x& = &26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)