Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+4)& = & -12 \color{red}{+} (-7+x) \\\Leftrightarrow & -18x+12& = &-12-7+x \\\Leftrightarrow & -18x \color{red}{+12} & = &-19 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -18x-x& = &-19-12 \\\Leftrightarrow & -19x& = &-31 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-31}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{31}{19} & & \\ & V = \left\{ \frac{31}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (2x+3)& = & -12 \color{red}{+} (-14-3x) \\\Leftrightarrow & 4x+6& = &-12-14-3x \\\Leftrightarrow & 4x \color{red}{+6} & = &-26 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-26 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 4x+3x& = &-26-6 \\\Leftrightarrow & 7x& = &-32 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-32}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-32}{7} & & \\ & V = \left\{ \frac{-32}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-3x+2)& = & -3 \color{red}{-} (-2-5x) \\\Leftrightarrow & -6x+4& = &-3+2+5x \\\Leftrightarrow & -6x \color{red}{+4} & = &-1 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & -6x-5x& = &-1-4 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x+6)& = & 8 \color{red}{+} (-15+x) \\\Leftrightarrow & 24x+24& = &8-15+x \\\Leftrightarrow & 24x \color{red}{+24} & = &-7 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &-7-24 \\\Leftrightarrow & 23x& = &-31 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-31}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-31}{23} & & \\ & V = \left\{ \frac{-31}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-5x+5)& = & -13 \color{red}{+} (-10+x) \\\Leftrightarrow & -10x+10& = &-13-10+x \\\Leftrightarrow & -10x \color{red}{+10} & = &-23 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -10x-x& = &-23-10 \\\Leftrightarrow & -11x& = &-33 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-33}{ \color{red}{-11} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x-6)& = & 3 \color{red}{-} (1-5x) \\\Leftrightarrow & 6x-12& = &3-1+5x \\\Leftrightarrow & 6x \color{red}{-12} & = &2 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 6x-5x& = &2+12 \\\Leftrightarrow & x& = &14 \\ & V = \left\{ 14 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+4)& = & -4 \color{red}{-} (-2+2x) \\\Leftrightarrow & 9x+12& = &-4+2-2x \\\Leftrightarrow & 9x \color{red}{+12} & = &-2 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & 9x+2x& = &-2-12 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x-7)& = & -1 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-14& = &-1-11+x \\\Leftrightarrow & -12x \color{red}{-14} & = &-12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -12x-x& = &-12+14 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+6)& = & 7 \color{red}{-} (-6+x) \\\Leftrightarrow & 30x+36& = &7+6-x \\\Leftrightarrow & 30x \color{red}{+36} & = &13 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &13-36 \\\Leftrightarrow & 31x& = &-23 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-23}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-23}{31} & & \\ & V = \left\{ \frac{-23}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x-5)& = & 6 \color{red}{+} (13+3x) \\\Leftrightarrow & -8x-20& = &6+13+3x \\\Leftrightarrow & -8x \color{red}{-20} & = &19 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -8x-3x& = &19+20 \\\Leftrightarrow & -11x& = &39 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{39}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-39}{11} & & \\ & V = \left\{ \frac{-39}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+5)& = & 4 \color{red}{+} (8-3x) \\\Leftrightarrow & 4x+20& = &4+8-3x \\\Leftrightarrow & 4x \color{red}{+20} & = &12 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 4x+3x& = &12-20 \\\Leftrightarrow & 7x& = &-8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (5x+5)& = & 15 \color{red}{-} (-13+3x) \\\Leftrightarrow & 10x+10& = &15+13-3x \\\Leftrightarrow & 10x \color{red}{+10} & = &28 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &28 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 10x+3x& = &28-10 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)