Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x+5)& = & -10 \color{red}{+} (-7+x) \\\Leftrightarrow & 2x+10& = &-10-7+x \\\Leftrightarrow & 2x \color{red}{+10} & = &-17 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 2x-x& = &-17-10 \\\Leftrightarrow & x& = &-27 \\ & V = \left\{ -27 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x+4)& = & -3 \color{red}{-} (13-5x) \\\Leftrightarrow & 36x+24& = &-3-13+5x \\\Leftrightarrow & 36x \color{red}{+24} & = &-16 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 36x-5x& = &-16-24 \\\Leftrightarrow & 31x& = &-40 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-40}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-40}{31} & & \\ & V = \left\{ \frac{-40}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (2x+6)& = & 12 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x+36& = &12+3-x \\\Leftrightarrow & 12x \color{red}{+36} & = &15 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 12x+x& = &15-36 \\\Leftrightarrow & 13x& = &-21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-1)& = & -13 \color{red}{+} (-9+x) \\\Leftrightarrow & 6x-3& = &-13-9+x \\\Leftrightarrow & 6x \color{red}{-3} & = &-22 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 6x-x& = &-22+3 \\\Leftrightarrow & 5x& = &-19 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-19}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-19}{5} & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-5)& = & 14 \color{red}{+} (-6+x) \\\Leftrightarrow & 30x-30& = &14-6+x \\\Leftrightarrow & 30x \color{red}{-30} & = &8 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &8+30 \\\Leftrightarrow & 29x& = &38 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{38}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{38}{29} & & \\ & V = \left\{ \frac{38}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-x+1)& = & 9 \color{red}{+} (3+x) \\\Leftrightarrow & -2x+2& = &9+3+x \\\Leftrightarrow & -2x \color{red}{+2} & = &12 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -2x-x& = &12-2 \\\Leftrightarrow & -3x& = &10 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{10}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-1)& = & -10 \color{red}{-} (-9-2x) \\\Leftrightarrow & -5x-5& = &-10+9+2x \\\Leftrightarrow & -5x \color{red}{-5} & = &-1 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & -5x-2x& = &-1+5 \\\Leftrightarrow & -7x& = &4 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{4}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x+7)& = & 11 \color{red}{-} (6-5x) \\\Leftrightarrow & 6x+21& = &11-6+5x \\\Leftrightarrow & 6x \color{red}{+21} & = &5 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & 6x-5x& = &5-21 \\\Leftrightarrow & x& = &-16 \\ & V = \left\{ -16 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x+1)& = & 1 \color{red}{+} (-12+x) \\\Leftrightarrow & 10x+2& = &1-12+x \\\Leftrightarrow & 10x \color{red}{+2} & = &-11 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 10x-x& = &-11-2 \\\Leftrightarrow & 9x& = &-13 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-13}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x-5)& = & 6 \color{red}{+} (-3+x) \\\Leftrightarrow & 2x-10& = &6-3+x \\\Leftrightarrow & 2x \color{red}{-10} & = &3 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 2x-x& = &3+10 \\\Leftrightarrow & x& = &13 \\ & V = \left\{ 13 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x-1)& = & 10 \color{red}{-} (-13+x) \\\Leftrightarrow & 30x-5& = &10+13-x \\\Leftrightarrow & 30x \color{red}{-5} & = &23 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 30x+x& = &23+5 \\\Leftrightarrow & 31x& = &28 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{28}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{28}{31} & & \\ & V = \left\{ \frac{28}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x-5)& = & 7 \color{red}{+} (5-4x) \\\Leftrightarrow & 5x-25& = &7+5-4x \\\Leftrightarrow & 5x \color{red}{-25} & = &12 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & 5x+4x& = &12+25 \\\Leftrightarrow & 9x& = &37 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{37}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{37}{9} & & \\ & V = \left\{ \frac{37}{9} \right\} & \\\end{align}\)