Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-2)& = & -10 \color{red}{-} (8-2x) \\\Leftrightarrow & 3x-6& = &-10-8+2x \\\Leftrightarrow & 3x \color{red}{-6} & = &-18 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & 3x-2x& = &-18+6 \\\Leftrightarrow & x& = &-12 \\ & V = \left\{ -12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x-6)& = & -13 \color{red}{-} (5+x) \\\Leftrightarrow & 24x-36& = &-13-5-x \\\Leftrightarrow & 24x \color{red}{-36} & = &-18 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &-18+36 \\\Leftrightarrow & 25x& = &18 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{18}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{18}{25} & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x+5)& = & -10 \color{red}{-} (4+x) \\\Leftrightarrow & 10x+10& = &-10-4-x \\\Leftrightarrow & 10x \color{red}{+10} & = &-14 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 10x+x& = &-14-10 \\\Leftrightarrow & 11x& = &-24 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-24}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-24}{11} & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-2x+5)& = & -1 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x+30& = &-1-6+x \\\Leftrightarrow & -12x \color{red}{+30} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -12x-x& = &-7-30 \\\Leftrightarrow & -13x& = &-37 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-37}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{37}{13} & & \\ & V = \left\{ \frac{37}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x-5)& = & 12 \color{red}{-} (-1-3x) \\\Leftrightarrow & -4x-20& = &12+1+3x \\\Leftrightarrow & -4x \color{red}{-20} & = &13 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -4x-3x& = &13+20 \\\Leftrightarrow & -7x& = &33 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{33}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-33}{7} & & \\ & V = \left\{ \frac{-33}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x-3)& = & -2 \color{red}{-} (-1+x) \\\Leftrightarrow & 10x-6& = &-2+1-x \\\Leftrightarrow & 10x \color{red}{-6} & = &-1 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 10x+x& = &-1+6 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x+3)& = & 1 \color{red}{-} (10+3x) \\\Leftrightarrow & 4x+6& = &1-10-3x \\\Leftrightarrow & 4x \color{red}{+6} & = &-9 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 4x+3x& = &-9-6 \\\Leftrightarrow & 7x& = &-15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x+6)& = & -13 \color{red}{-} (10+x) \\\Leftrightarrow & -24x+24& = &-13-10-x \\\Leftrightarrow & -24x \color{red}{+24} & = &-23 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &-23-24 \\\Leftrightarrow & -23x& = &-47 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-47}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{47}{23} & & \\ & V = \left\{ \frac{47}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+5)& = & -15 \color{red}{+} (-9+3x) \\\Leftrightarrow & -5x+25& = &-15-9+3x \\\Leftrightarrow & -5x \color{red}{+25} & = &-24 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{-3x} & = &-24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-25} \\\Leftrightarrow & -5x-3x& = &-24-25 \\\Leftrightarrow & -8x& = &-49 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-49}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{49}{8} & & \\ & V = \left\{ \frac{49}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x+1)& = & -10 \color{red}{-} (-10+x) \\\Leftrightarrow & 20x+5& = &-10+10-x \\\Leftrightarrow & 20x \color{red}{+5} & = &0 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 20x+x& = &0-5 \\\Leftrightarrow & 21x& = &-5 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-5}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{21} & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-1)& = & 1 \color{red}{+} (-15+x) \\\Leftrightarrow & -20x-4& = &1-15+x \\\Leftrightarrow & -20x \color{red}{-4} & = &-14 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -20x-x& = &-14+4 \\\Leftrightarrow & -21x& = &-10 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-10}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-4)& = & -4 \color{red}{+} (-11+x) \\\Leftrightarrow & -10x-20& = &-4-11+x \\\Leftrightarrow & -10x \color{red}{-20} & = &-15 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -10x-x& = &-15+20 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)