Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x+5)& = & 12 \color{red}{-} (-14+2x) \\\Leftrightarrow & -3x+15& = &12+14-2x \\\Leftrightarrow & -3x \color{red}{+15} & = &26 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &26 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & -3x+2x& = &26-15 \\\Leftrightarrow & -x& = &11 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{11}{ \color{red}{-1} } \\\Leftrightarrow & x = -11 & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-6)& = & -6 \color{red}{+} (-12+x) \\\Leftrightarrow & 12x-18& = &-6-12+x \\\Leftrightarrow & 12x \color{red}{-18} & = &-18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &-18+18 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-5)& = & 7 \color{red}{-} (-12+3x) \\\Leftrightarrow & 4x-10& = &7+12-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &19 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &19+10 \\\Leftrightarrow & 7x& = &29 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{29}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x+4)& = & -13 \color{red}{+} (-13-2x) \\\Leftrightarrow & -9x+12& = &-13-13-2x \\\Leftrightarrow & -9x \color{red}{+12} & = &-26 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &-26 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & -9x+2x& = &-26-12 \\\Leftrightarrow & -7x& = &-38 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-38}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{38}{7} & & \\ & V = \left\{ \frac{38}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-6)& = & -8 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x-24& = &-8-7+x \\\Leftrightarrow & 12x \color{red}{-24} & = &-15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &-15+24 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+2)& = & 15 \color{red}{+} (10+x) \\\Leftrightarrow & 5x+10& = &15+10+x \\\Leftrightarrow & 5x \color{red}{+10} & = &25 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 5x-x& = &25-10 \\\Leftrightarrow & 4x& = &15 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{15}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{15}{4} & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-1)& = & -5 \color{red}{-} (11-5x) \\\Leftrightarrow & 8x-4& = &-5-11+5x \\\Leftrightarrow & 8x \color{red}{-4} & = &-16 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 8x-5x& = &-16+4 \\\Leftrightarrow & 3x& = &-12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-12}{ \color{red}{3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x-6)& = & -5 \color{red}{+} (15-3x) \\\Leftrightarrow & -4x-24& = &-5+15-3x \\\Leftrightarrow & -4x \color{red}{-24} & = &10 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & -4x+3x& = &10+24 \\\Leftrightarrow & -x& = &34 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{34}{ \color{red}{-1} } \\\Leftrightarrow & x = -34 & & \\ & V = \left\{ -34 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-1)& = & -9 \color{red}{+} (5+x) \\\Leftrightarrow & -18x-3& = &-9+5+x \\\Leftrightarrow & -18x \color{red}{-3} & = &-4 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -18x-x& = &-4+3 \\\Leftrightarrow & -19x& = &-1 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-1}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{1}{19} & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-2)& = & -3 \color{red}{+} (-11+3x) \\\Leftrightarrow & 20x-10& = &-3-11+3x \\\Leftrightarrow & 20x \color{red}{-10} & = &-14 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 20x-3x& = &-14+10 \\\Leftrightarrow & 17x& = &-4 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-4}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x+2)& = & -4 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x+8& = &-4+11-x \\\Leftrightarrow & 12x \color{red}{+8} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &7-8 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x-4)& = & -15 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-16& = &-15-11+x \\\Leftrightarrow & -12x \color{red}{-16} & = &-26 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -12x-x& = &-26+16 \\\Leftrightarrow & -13x& = &-10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)