Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-4x-7)& = & -15 \color{red}{-} (-13+3x) \\\Leftrightarrow & -16x-28& = &-15+13-3x \\\Leftrightarrow & -16x \color{red}{-28} & = &-2 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & -16x+3x& = &-2+28 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x-3)& = & -10 \color{red}{+} (6-3x) \\\Leftrightarrow & 4x-12& = &-10+6-3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-4 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 4x+3x& = &-4+12 \\\Leftrightarrow & 7x& = &8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x-1)& = & 14 \color{red}{-} (-11+x) \\\Leftrightarrow & -18x-6& = &14+11-x \\\Leftrightarrow & -18x \color{red}{-6} & = &25 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -18x+x& = &25+6 \\\Leftrightarrow & -17x& = &31 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{31}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-31}{17} & & \\ & V = \left\{ \frac{-31}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x+5)& = & 11 \color{red}{-} (-2+x) \\\Leftrightarrow & 3x+15& = &11+2-x \\\Leftrightarrow & 3x \color{red}{+15} & = &13 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 3x+x& = &13-15 \\\Leftrightarrow & 4x& = &-2 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-2}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-3x+6)& = & -5 \color{red}{-} (-7+x) \\\Leftrightarrow & -12x+24& = &-5+7-x \\\Leftrightarrow & -12x \color{red}{+24} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -12x+x& = &2-24 \\\Leftrightarrow & -11x& = &-22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-22}{ \color{red}{-11} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-2)& = & -2 \color{red}{-} (-9+x) \\\Leftrightarrow & -36x-12& = &-2+9-x \\\Leftrightarrow & -36x \color{red}{-12} & = &7 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -36x+x& = &7+12 \\\Leftrightarrow & -35x& = &19 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{19}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-19}{35} & & \\ & V = \left\{ \frac{-19}{35} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x+3)& = & -10 \color{red}{-} (-3+x) \\\Leftrightarrow & 18x+9& = &-10+3-x \\\Leftrightarrow & 18x \color{red}{+9} & = &-7 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 18x+x& = &-7-9 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x+1)& = & -3 \color{red}{-} (6+x) \\\Leftrightarrow & 25x+5& = &-3-6-x \\\Leftrightarrow & 25x \color{red}{+5} & = &-9 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 25x+x& = &-9-5 \\\Leftrightarrow & 26x& = &-14 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-14}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-3)& = & 1 \color{red}{-} (5-5x) \\\Leftrightarrow & 8x-6& = &1-5+5x \\\Leftrightarrow & 8x \color{red}{-6} & = &-4 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 8x-5x& = &-4+6 \\\Leftrightarrow & 3x& = &2 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{2}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x-7)& = & -4 \color{red}{-} (3+3x) \\\Leftrightarrow & 4x-14& = &-4-3-3x \\\Leftrightarrow & 4x \color{red}{-14} & = &-7 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 4x+3x& = &-7+14 \\\Leftrightarrow & 7x& = &7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{7}{ \color{red}{7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-6)& = & -6 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x-12& = &-6-2+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-8+12 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+3)& = & 15 \color{red}{+} (6+4x) \\\Leftrightarrow & 9x+9& = &15+6+4x \\\Leftrightarrow & 9x \color{red}{+9} & = &21 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+9} \color{blue}{-9} \color{blue}{-4x} & = &21 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-9} \\\Leftrightarrow & 9x-4x& = &21-9 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)