Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x+2)& = & -11 \color{red}{+} (10+x) \\\Leftrightarrow & 6x+6& = &-11+10+x \\\Leftrightarrow & 6x \color{red}{+6} & = &-1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &-1-6 \\\Leftrightarrow & 5x& = &-7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (2x+3)& = & -14 \color{red}{-} (-10-3x) \\\Leftrightarrow & 4x+6& = &-14+10+3x \\\Leftrightarrow & 4x \color{red}{+6} & = &-4 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 4x-3x& = &-4-6 \\\Leftrightarrow & x& = &-10 \\ & V = \left\{ -10 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x+3)& = & -10 \color{red}{+} (6-4x) \\\Leftrightarrow & -25x+15& = &-10+6-4x \\\Leftrightarrow & -25x \color{red}{+15} & = &-4 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -25x+4x& = &-4-15 \\\Leftrightarrow & -21x& = &-19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+7)& = & 11 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+28& = &11+2-x \\\Leftrightarrow & -12x \color{red}{+28} & = &13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -12x+x& = &13-28 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x-2)& = & 2 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x-4& = &2+9-x \\\Leftrightarrow & 12x \color{red}{-4} & = &11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &11+4 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x+4)& = & -14 \color{red}{-} (7+x) \\\Leftrightarrow & 30x+20& = &-14-7-x \\\Leftrightarrow & 30x \color{red}{+20} & = &-21 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 30x+x& = &-21-20 \\\Leftrightarrow & 31x& = &-41 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-41}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-41}{31} & & \\ & V = \left\{ \frac{-41}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-2)& = & -13 \color{red}{+} (-9-4x) \\\Leftrightarrow & -5x-10& = &-13-9-4x \\\Leftrightarrow & -5x \color{red}{-10} & = &-22 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &-22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & -5x+4x& = &-22+10 \\\Leftrightarrow & -x& = &-12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-12}{ \color{red}{-1} } \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-7)& = & 8 \color{red}{+} (8-2x) \\\Leftrightarrow & 3x-21& = &8+8-2x \\\Leftrightarrow & 3x \color{red}{-21} & = &16 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+21} \\\Leftrightarrow & 3x+2x& = &16+21 \\\Leftrightarrow & 5x& = &37 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{37}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{37}{5} & & \\ & V = \left\{ \frac{37}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x+7)& = & 14 \color{red}{-} (4+x) \\\Leftrightarrow & -20x+28& = &14-4-x \\\Leftrightarrow & -20x \color{red}{+28} & = &10 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -20x+x& = &10-28 \\\Leftrightarrow & -19x& = &-18 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-18}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{18}{19} & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x+3)& = & -13 \color{red}{+} (9-3x) \\\Leftrightarrow & -4x+6& = &-13+9-3x \\\Leftrightarrow & -4x \color{red}{+6} & = &-4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & -4x+3x& = &-4-6 \\\Leftrightarrow & -x& = &-10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-10}{ \color{red}{-1} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x+6)& = & -11 \color{red}{+} (-3+x) \\\Leftrightarrow & -5x+30& = &-11-3+x \\\Leftrightarrow & -5x \color{red}{+30} & = &-14 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -5x-x& = &-14-30 \\\Leftrightarrow & -6x& = &-44 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{-44}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{22}{3} & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x+1)& = & -5 \color{red}{+} (-9+x) \\\Leftrightarrow & -24x+6& = &-5-9+x \\\Leftrightarrow & -24x \color{red}{+6} & = &-14 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -24x-x& = &-14-6 \\\Leftrightarrow & -25x& = &-20 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-20}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)