Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-6x-4)=13+(-10+x)\)
2. \(4(-5x-7)=-7-(-6+3x)\)
3. \(2(x-6)=-15+(-10+x)\)
4. \(3(-2x-5)=13-(-6-5x)\)
5. \(4(6x+1)=-15+(12+x)\)
6. \(2(5x+2)=14+(-11-3x)\)
7. \(5(5x+7)=-10-(-12+x)\)
8. \(5(x+2)=-13+(14-2x)\)
9. \(4(2x-2)=-12-(3+3x)\)
10. \(4(-4x-2)=-15+(2-3x)\)
11. \(3(3x-7)=12+(11+4x)\)
12. \(5(2x-7)=10-(-14-3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-4)& = & 13 \color{red}{+} (-10+x) \\\Leftrightarrow & -18x-12& = &13-10+x \\\Leftrightarrow & -18x \color{red}{-12} & = &3 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -18x-x& = &3+12 \\\Leftrightarrow & -19x& = &15 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{15}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-15}{19} & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x-7)& = & -7 \color{red}{-} (-6+3x) \\\Leftrightarrow & -20x-28& = &-7+6-3x \\\Leftrightarrow & -20x \color{red}{-28} & = &-1 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & -20x+3x& = &-1+28 \\\Leftrightarrow & -17x& = &27 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{27}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-27}{17} & & \\ & V = \left\{ \frac{-27}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x-6)& = & -15 \color{red}{+} (-10+x) \\\Leftrightarrow & 2x-12& = &-15-10+x \\\Leftrightarrow & 2x \color{red}{-12} & = &-25 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 2x-x& = &-25+12 \\\Leftrightarrow & x& = &-13 \\ & V = \left\{ -13 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x-5)& = & 13 \color{red}{-} (-6-5x) \\\Leftrightarrow & -6x-15& = &13+6+5x \\\Leftrightarrow & -6x \color{red}{-15} & = &19 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+15} \\\Leftrightarrow & -6x-5x& = &19+15 \\\Leftrightarrow & -11x& = &34 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{34}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-34}{11} & & \\ & V = \left\{ \frac{-34}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x+1)& = & -15 \color{red}{+} (12+x) \\\Leftrightarrow & 24x+4& = &-15+12+x \\\Leftrightarrow & 24x \color{red}{+4} & = &-3 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 24x-x& = &-3-4 \\\Leftrightarrow & 23x& = &-7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-7}{23} & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x+2)& = & 14 \color{red}{+} (-11-3x) \\\Leftrightarrow & 10x+4& = &14-11-3x \\\Leftrightarrow & 10x \color{red}{+4} & = &3 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 10x+3x& = &3-4 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x+7)& = & -10 \color{red}{-} (-12+x) \\\Leftrightarrow & 25x+35& = &-10+12-x \\\Leftrightarrow & 25x \color{red}{+35} & = &2 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 25x+x& = &2-35 \\\Leftrightarrow & 26x& = &-33 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-33}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-33}{26} & & \\ & V = \left\{ \frac{-33}{26} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x+2)& = & -13 \color{red}{+} (14-2x) \\\Leftrightarrow & 5x+10& = &-13+14-2x \\\Leftrightarrow & 5x \color{red}{+10} & = &1 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & 5x+2x& = &1-10 \\\Leftrightarrow & 7x& = &-9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x-2)& = & -12 \color{red}{-} (3+3x) \\\Leftrightarrow & 8x-8& = &-12-3-3x \\\Leftrightarrow & 8x \color{red}{-8} & = &-15 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 8x+3x& = &-15+8 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-2)& = & -15 \color{red}{+} (2-3x) \\\Leftrightarrow & -16x-8& = &-15+2-3x \\\Leftrightarrow & -16x \color{red}{-8} & = &-13 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -16x+3x& = &-13+8 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x-7)& = & 12 \color{red}{+} (11+4x) \\\Leftrightarrow & 9x-21& = &12+11+4x \\\Leftrightarrow & 9x \color{red}{-21} & = &23 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &23 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & 9x-4x& = &23+21 \\\Leftrightarrow & 5x& = &44 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{44}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{44}{5} & & \\ & V = \left\{ \frac{44}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x-7)& = & 10 \color{red}{-} (-14-3x) \\\Leftrightarrow & 10x-35& = &10+14+3x \\\Leftrightarrow & 10x \color{red}{-35} & = &24 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 10x-3x& = &24+35 \\\Leftrightarrow & 7x& = &59 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{59}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{59}{7} & & \\ & V = \left\{ \frac{59}{7} \right\} & \\\end{align}\)