Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x+5)& = & -2 \color{red}{-} (15+x) \\\Leftrightarrow & 9x+15& = &-2-15-x \\\Leftrightarrow & 9x \color{red}{+15} & = &-17 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 9x+x& = &-17-15 \\\Leftrightarrow & 10x& = &-32 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-32}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-16}{5} & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (2x-2)& = & -14 \color{red}{-} (-3-3x) \\\Leftrightarrow & 4x-4& = &-14+3+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &-11 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &-11+4 \\\Leftrightarrow & x& = &-7 \\ & V = \left\{ -7 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x+7)& = & -8 \color{red}{-} (2+3x) \\\Leftrightarrow & 10x+14& = &-8-2-3x \\\Leftrightarrow & 10x \color{red}{+14} & = &-10 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 10x+3x& = &-10-14 \\\Leftrightarrow & 13x& = &-24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x+7)& = & 14 \color{red}{-} (8+x) \\\Leftrightarrow & 25x+35& = &14-8-x \\\Leftrightarrow & 25x \color{red}{+35} & = &6 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 25x+x& = &6-35 \\\Leftrightarrow & 26x& = &-29 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-29}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-29}{26} & & \\ & V = \left\{ \frac{-29}{26} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x-6)& = & 6 \color{red}{-} (-15-2x) \\\Leftrightarrow & 25x-30& = &6+15+2x \\\Leftrightarrow & 25x \color{red}{-30} & = &21 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &21 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & 25x-2x& = &21+30 \\\Leftrightarrow & 23x& = &51 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{51}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{51}{23} & & \\ & V = \left\{ \frac{51}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x+1)& = & 10 \color{red}{+} (-7+3x) \\\Leftrightarrow & 10x+2& = &10-7+3x \\\Leftrightarrow & 10x \color{red}{+2} & = &3 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 10x-3x& = &3-2 \\\Leftrightarrow & 7x& = &1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x+1)& = & 12 \color{red}{-} (-6+x) \\\Leftrightarrow & -18x+3& = &12+6-x \\\Leftrightarrow & -18x \color{red}{+3} & = &18 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -18x+x& = &18-3 \\\Leftrightarrow & -17x& = &15 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{15}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-15}{17} & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x+3)& = & -2 \color{red}{-} (-2+x) \\\Leftrightarrow & -20x+12& = &-2+2-x \\\Leftrightarrow & -20x \color{red}{+12} & = &0 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -20x+x& = &0-12 \\\Leftrightarrow & -19x& = &-12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{12}{19} & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x+6)& = & 3 \color{red}{-} (-8+3x) \\\Leftrightarrow & -20x+24& = &3+8-3x \\\Leftrightarrow & -20x \color{red}{+24} & = &11 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -20x+3x& = &11-24 \\\Leftrightarrow & -17x& = &-13 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-13}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{13}{17} & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x+6)& = & 6 \color{red}{-} (6+x) \\\Leftrightarrow & -6x+18& = &6-6-x \\\Leftrightarrow & -6x \color{red}{+18} & = &0 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &0-18 \\\Leftrightarrow & -5x& = &-18 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-18}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+7)& = & -14 \color{red}{-} (5-3x) \\\Leftrightarrow & -4x+14& = &-14-5+3x \\\Leftrightarrow & -4x \color{red}{+14} & = &-19 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -4x-3x& = &-19-14 \\\Leftrightarrow & -7x& = &-33 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-33}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{33}{7} & & \\ & V = \left\{ \frac{33}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-6x+2)& = & -11 \color{red}{-} (8+x) \\\Leftrightarrow & -36x+12& = &-11-8-x \\\Leftrightarrow & -36x \color{red}{+12} & = &-19 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -36x+x& = &-19-12 \\\Leftrightarrow & -35x& = &-31 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-31}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{31}{35} & & \\ & V = \left\{ \frac{31}{35} \right\} & \\\end{align}\)