Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

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