Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x+6)& = & 9 \color{red}{-} (-15+x) \\\Leftrightarrow & -25x+30& = &9+15-x \\\Leftrightarrow & -25x \color{red}{+30} & = &24 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -25x+x& = &24-30 \\\Leftrightarrow & -24x& = &-6 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{-6}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x+4)& = & -14 \color{red}{+} (-7+x) \\\Leftrightarrow & -9x+12& = &-14-7+x \\\Leftrightarrow & -9x \color{red}{+12} & = &-21 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -9x-x& = &-21-12 \\\Leftrightarrow & -10x& = &-33 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-33}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{33}{10} & & \\ & V = \left\{ \frac{33}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+2)& = & -15 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x+12& = &-15+11-x \\\Leftrightarrow & -24x \color{red}{+12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &-4-12 \\\Leftrightarrow & -23x& = &-16 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-16}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+4)& = & -3 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+16& = &-3+10-x \\\Leftrightarrow & -12x \color{red}{+16} & = &7 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -12x+x& = &7-16 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-1)& = & -8 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x-3& = &-8+1-x \\\Leftrightarrow & -12x \color{red}{-3} & = &-7 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -12x+x& = &-7+3 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x-3)& = & -4 \color{red}{-} (-8+x) \\\Leftrightarrow & 2x-6& = &-4+8-x \\\Leftrightarrow & 2x \color{red}{-6} & = &4 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 2x+x& = &4+6 \\\Leftrightarrow & 3x& = &10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+3)& = & -8 \color{red}{-} (1+x) \\\Leftrightarrow & -30x+15& = &-8-1-x \\\Leftrightarrow & -30x \color{red}{+15} & = &-9 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &-9-15 \\\Leftrightarrow & -29x& = &-24 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-24}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{24}{29} & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x-1)& = & -13 \color{red}{+} (9+x) \\\Leftrightarrow & -24x-4& = &-13+9+x \\\Leftrightarrow & -24x \color{red}{-4} & = &-4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -24x-x& = &-4+4 \\\Leftrightarrow & -25x& = &0 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{0}{ \color{red}{-25} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+1)& = & -9 \color{red}{-} (10+x) \\\Leftrightarrow & 3x+3& = &-9-10-x \\\Leftrightarrow & 3x \color{red}{+3} & = &-19 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 3x+x& = &-19-3 \\\Leftrightarrow & 4x& = &-22 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-22}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-11}{2} & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x-7)& = & 7 \color{red}{+} (-15-2x) \\\Leftrightarrow & -15x-35& = &7-15-2x \\\Leftrightarrow & -15x \color{red}{-35} & = &-8 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &-8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & -15x+2x& = &-8+35 \\\Leftrightarrow & -13x& = &27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x-6)& = & 12 \color{red}{-} (1+x) \\\Leftrightarrow & 12x-24& = &12-1-x \\\Leftrightarrow & 12x \color{red}{-24} & = &11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &11+24 \\\Leftrightarrow & 13x& = &35 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{35}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+1)& = & 11 \color{red}{-} (13-3x) \\\Leftrightarrow & 10x+5& = &11-13+3x \\\Leftrightarrow & 10x \color{red}{+5} & = &-2 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & 10x-3x& = &-2-5 \\\Leftrightarrow & 7x& = &-7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-7}{ \color{red}{7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)