Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x-4)& = & 6 \color{red}{+} (4+x) \\\Leftrightarrow & -25x-20& = &6+4+x \\\Leftrightarrow & -25x \color{red}{-20} & = &10 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -25x-x& = &10+20 \\\Leftrightarrow & -26x& = &30 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{30}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x+4)& = & 15 \color{red}{-} (-13+x) \\\Leftrightarrow & -20x+20& = &15+13-x \\\Leftrightarrow & -20x \color{red}{+20} & = &28 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -20x+x& = &28-20 \\\Leftrightarrow & -19x& = &8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+1)& = & -11 \color{red}{-} (10-3x) \\\Leftrightarrow & -4x+2& = &-11-10+3x \\\Leftrightarrow & -4x \color{red}{+2} & = &-21 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -4x-3x& = &-21-2 \\\Leftrightarrow & -7x& = &-23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+1)& = & -7 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x+4& = &-7+10-x \\\Leftrightarrow & -24x \color{red}{+4} & = &3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -24x+x& = &3-4 \\\Leftrightarrow & -23x& = &-1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-6)& = & -13 \color{red}{+} (-12+3x) \\\Leftrightarrow & 4x-24& = &-13-12+3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-25 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & 4x-3x& = &-25+24 \\\Leftrightarrow & x& = &-1 \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x+4)& = & 12 \color{red}{+} (-12-4x) \\\Leftrightarrow & -9x+12& = &12-12-4x \\\Leftrightarrow & -9x \color{red}{+12} & = &0 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+4x} & = &0 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-12} \\\Leftrightarrow & -9x+4x& = &0-12 \\\Leftrightarrow & -5x& = &-12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x-5)& = & -11 \color{red}{-} (-2+x) \\\Leftrightarrow & 20x-20& = &-11+2-x \\\Leftrightarrow & 20x \color{red}{-20} & = &-9 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 20x+x& = &-9+20 \\\Leftrightarrow & 21x& = &11 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{11}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{11}{21} & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x+1)& = & -5 \color{red}{+} (10-2x) \\\Leftrightarrow & -3x+3& = &-5+10-2x \\\Leftrightarrow & -3x \color{red}{+3} & = &5 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & -3x+2x& = &5-3 \\\Leftrightarrow & -x& = &2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{2}{ \color{red}{-1} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x-2)& = & -7 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x-6& = &-7+1-x \\\Leftrightarrow & 12x \color{red}{-6} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &-6+6 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-7)& = & 2 \color{red}{-} (15+x) \\\Leftrightarrow & -24x-28& = &2-15-x \\\Leftrightarrow & -24x \color{red}{-28} & = &-13 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -24x+x& = &-13+28 \\\Leftrightarrow & -23x& = &15 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{15}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-15}{23} & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-7)& = & -14 \color{red}{-} (3+x) \\\Leftrightarrow & -6x-42& = &-14-3-x \\\Leftrightarrow & -6x \color{red}{-42} & = &-17 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -6x+x& = &-17+42 \\\Leftrightarrow & -5x& = &25 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{25}{ \color{red}{-5} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x+4)& = & -7 \color{red}{+} (2+x) \\\Leftrightarrow & 12x+8& = &-7+2+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-5-8 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)