Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x-5)& = & 5 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x-30& = &5-4+x \\\Leftrightarrow & -24x \color{red}{-30} & = &1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -24x-x& = &1+30 \\\Leftrightarrow & -25x& = &31 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{31}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-31}{25} & & \\ & V = \left\{ \frac{-31}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+6)& = & 12 \color{red}{+} (-3+x) \\\Leftrightarrow & -24x+36& = &12-3+x \\\Leftrightarrow & -24x \color{red}{+36} & = &9 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -24x-x& = &9-36 \\\Leftrightarrow & -25x& = &-27 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-27}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{27}{25} & & \\ & V = \left\{ \frac{27}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x+7)& = & -8 \color{red}{-} (7-3x) \\\Leftrightarrow & 4x+14& = &-8-7+3x \\\Leftrightarrow & 4x \color{red}{+14} & = &-15 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 4x-3x& = &-15-14 \\\Leftrightarrow & x& = &-29 \\ & V = \left\{ -29 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x+5)& = & -10 \color{red}{-} (-3+3x) \\\Leftrightarrow & -8x+10& = &-10+3-3x \\\Leftrightarrow & -8x \color{red}{+10} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -8x+3x& = &-7-10 \\\Leftrightarrow & -5x& = &-17 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-17}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{17}{5} & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x-4)& = & -6 \color{red}{-} (-2+x) \\\Leftrightarrow & 6x-8& = &-6+2-x \\\Leftrightarrow & 6x \color{red}{-8} & = &-4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 6x+x& = &-4+8 \\\Leftrightarrow & 7x& = &4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x+1)& = & 11 \color{red}{+} (12-5x) \\\Leftrightarrow & -6x+3& = &11+12-5x \\\Leftrightarrow & -6x \color{red}{+3} & = &23 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & -6x+5x& = &23-3 \\\Leftrightarrow & -x& = &20 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{20}{ \color{red}{-1} } \\\Leftrightarrow & x = -20 & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x+1)& = & 8 \color{red}{-} (-13+x) \\\Leftrightarrow & 25x+5& = &8+13-x \\\Leftrightarrow & 25x \color{red}{+5} & = &21 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 25x+x& = &21-5 \\\Leftrightarrow & 26x& = &16 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{16}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-x+5)& = & 1 \color{red}{+} (10-4x) \\\Leftrightarrow & -5x+25& = &1+10-4x \\\Leftrightarrow & -5x \color{red}{+25} & = &11 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-25} \\\Leftrightarrow & -5x+4x& = &11-25 \\\Leftrightarrow & -x& = &-14 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-14}{ \color{red}{-1} } \\\Leftrightarrow & x = 14 & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-5)& = & 7 \color{red}{+} (-4+x) \\\Leftrightarrow & 12x-30& = &7-4+x \\\Leftrightarrow & 12x \color{red}{-30} & = &3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 12x-x& = &3+30 \\\Leftrightarrow & 11x& = &33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{33}{ \color{red}{11} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x-4)& = & -7 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x-8& = &-7+15-x \\\Leftrightarrow & -12x \color{red}{-8} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -12x+x& = &8+8 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x-1)& = & 12 \color{red}{-} (10+x) \\\Leftrightarrow & -5x-5& = &12-10-x \\\Leftrightarrow & -5x \color{red}{-5} & = &2 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -5x+x& = &2+5 \\\Leftrightarrow & -4x& = &7 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{7}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-7}{4} & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x+4)& = & 1 \color{red}{+} (-15+x) \\\Leftrightarrow & -20x+20& = &1-15+x \\\Leftrightarrow & -20x \color{red}{+20} & = &-14 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &-14-20 \\\Leftrightarrow & -21x& = &-34 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-34}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{34}{21} & & \\ & V = \left\{ \frac{34}{21} \right\} & \\\end{align}\)