Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-4)& = & -5 \color{red}{+} (1+x) \\\Leftrightarrow & -2x-8& = &-5+1+x \\\Leftrightarrow & -2x \color{red}{-8} & = &-4 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -2x-x& = &-4+8 \\\Leftrightarrow & -3x& = &4 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{4}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+5)& = & -10 \color{red}{-} (-15+x) \\\Leftrightarrow & 6x+15& = &-10+15-x \\\Leftrightarrow & 6x \color{red}{+15} & = &5 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 6x+x& = &5-15 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x+7)& = & 8 \color{red}{-} (6+x) \\\Leftrightarrow & -18x+21& = &8-6-x \\\Leftrightarrow & -18x \color{red}{+21} & = &2 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -18x+x& = &2-21 \\\Leftrightarrow & -17x& = &-19 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-19}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{19}{17} & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+2)& = & 5 \color{red}{-} (7-5x) \\\Leftrightarrow & 6x+6& = &5-7+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &-2-6 \\\Leftrightarrow & x& = &-8 \\ & V = \left\{ -8 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-3)& = & 14 \color{red}{-} (1+x) \\\Leftrightarrow & -8x-12& = &14-1-x \\\Leftrightarrow & -8x \color{red}{-12} & = &13 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -8x+x& = &13+12 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x-4)& = & -8 \color{red}{-} (1+x) \\\Leftrightarrow & 12x-24& = &-8-1-x \\\Leftrightarrow & 12x \color{red}{-24} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &-9+24 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x-5)& = & -14 \color{red}{-} (12+x) \\\Leftrightarrow & 25x-25& = &-14-12-x \\\Leftrightarrow & 25x \color{red}{-25} & = &-26 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 25x+x& = &-26+25 \\\Leftrightarrow & 26x& = &-1 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-1}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-1}{26} & & \\ & V = \left\{ \frac{-1}{26} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x+6)& = & 10 \color{red}{+} (-8+x) \\\Leftrightarrow & -6x+18& = &10-8+x \\\Leftrightarrow & -6x \color{red}{+18} & = &2 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -6x-x& = &2-18 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x+5)& = & -14 \color{red}{-} (5+x) \\\Leftrightarrow & -6x+30& = &-14-5-x \\\Leftrightarrow & -6x \color{red}{+30} & = &-19 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -6x+x& = &-19-30 \\\Leftrightarrow & -5x& = &-49 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-49}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{49}{5} & & \\ & V = \left\{ \frac{49}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x+4)& = & -15 \color{red}{-} (-1+x) \\\Leftrightarrow & -24x+16& = &-15+1-x \\\Leftrightarrow & -24x \color{red}{+16} & = &-14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &-14-16 \\\Leftrightarrow & -23x& = &-30 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-30}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{30}{23} & & \\ & V = \left\{ \frac{30}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (2x+3)& = & 15 \color{red}{+} (3+x) \\\Leftrightarrow & 10x+15& = &15+3+x \\\Leftrightarrow & 10x \color{red}{+15} & = &18 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 10x-x& = &18-15 \\\Leftrightarrow & 9x& = &3 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{3}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x+2)& = & -9 \color{red}{+} (-5+x) \\\Leftrightarrow & -24x+12& = &-9-5+x \\\Leftrightarrow & -24x \color{red}{+12} & = &-14 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &-14-12 \\\Leftrightarrow & -25x& = &-26 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-26}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{26}{25} & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)