Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+5)& = & -11 \color{red}{+} (8+x) \\\Leftrightarrow & -12x+10& = &-11+8+x \\\Leftrightarrow & -12x \color{red}{+10} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -12x-x& = &-3-10 \\\Leftrightarrow & -13x& = &-13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-13}{ \color{red}{-13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x-2)& = & 9 \color{red}{+} (-13+x) \\\Leftrightarrow & -12x-8& = &9-13+x \\\Leftrightarrow & -12x \color{red}{-8} & = &-4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &-4+8 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x+1)& = & -10 \color{red}{+} (-5-5x) \\\Leftrightarrow & 8x+4& = &-10-5-5x \\\Leftrightarrow & 8x \color{red}{+4} & = &-15 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & 8x+5x& = &-15-4 \\\Leftrightarrow & 13x& = &-19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-2x-5)& = & 15 \color{red}{-} (-14+x) \\\Leftrightarrow & -8x-20& = &15+14-x \\\Leftrightarrow & -8x \color{red}{-20} & = &29 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &29 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -8x+x& = &29+20 \\\Leftrightarrow & -7x& = &49 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{49}{ \color{red}{-7} } \\\Leftrightarrow & x = -7 & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (4x-2)& = & -4 \color{red}{+} (3+x) \\\Leftrightarrow & 12x-6& = &-4+3+x \\\Leftrightarrow & 12x \color{red}{-6} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 12x-x& = &-1+6 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x+2)& = & 9 \color{red}{+} (7-2x) \\\Leftrightarrow & -5x+10& = &9+7-2x \\\Leftrightarrow & -5x \color{red}{+10} & = &16 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & -5x+2x& = &16-10 \\\Leftrightarrow & -3x& = &6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{6}{ \color{red}{-3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-3)& = & 11 \color{red}{-} (4+x) \\\Leftrightarrow & 6x-18& = &11-4-x \\\Leftrightarrow & 6x \color{red}{-18} & = &7 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 6x+x& = &7+18 \\\Leftrightarrow & 7x& = &25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x+3)& = & 1 \color{red}{-} (8-4x) \\\Leftrightarrow & 25x+15& = &1-8+4x \\\Leftrightarrow & 25x \color{red}{+15} & = &-7 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &-7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 25x-4x& = &-7-15 \\\Leftrightarrow & 21x& = &-22 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-22}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-22}{21} & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (6x-4)& = & -11 \color{red}{+} (-14+x) \\\Leftrightarrow & 30x-20& = &-11-14+x \\\Leftrightarrow & 30x \color{red}{-20} & = &-25 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 30x-x& = &-25+20 \\\Leftrightarrow & 29x& = &-5 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-5}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-5}{29} & & \\ & V = \left\{ \frac{-5}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x-4)& = & -3 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x-16& = &-3+5-x \\\Leftrightarrow & 12x \color{red}{-16} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 12x+x& = &2+16 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x+3)& = & 4 \color{red}{+} (-10-5x) \\\Leftrightarrow & -6x+18& = &4-10-5x \\\Leftrightarrow & -6x \color{red}{+18} & = &-6 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -6x+5x& = &-6-18 \\\Leftrightarrow & -x& = &-24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-24}{ \color{red}{-1} } \\\Leftrightarrow & x = 24 & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-2)& = & -9 \color{red}{+} (-13+x) \\\Leftrightarrow & -10x-10& = &-9-13+x \\\Leftrightarrow & -10x \color{red}{-10} & = &-22 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -10x-x& = &-22+10 \\\Leftrightarrow & -11x& = &-12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)