Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(3x+4)=-14+(7+x)\)
2. \(5(-x-6)=13+(-4-4x)\)
3. \(5(x-6)=14+(7+x)\)
4. \(6(5x-5)=9-(13+29x)\)
5. \(3(-4x-1)=-5+(5+11x)\)
6. \(6(2x+3)=6+(12+5x)\)
7. \(3(-6x-2)=15+(14+x)\)
8. \(3(-3x-7)=-5+(5-2x)\)
9. \(3(x-4)=4+(6+5x)\)
10. \(2(-5x-5)=2-(-3-3x)\)
11. \(6(-6x+6)=9-(7-5x)\)
12. \(5(3x+7)=3-(-9+4x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+4)& = & -14 \color{red}{+} (7+x) \\\Leftrightarrow & 18x+24& = &-14+7+x \\\Leftrightarrow & 18x \color{red}{+24} & = &-7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 18x-x& = &-7-24 \\\Leftrightarrow & 17x& = &-31 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-31}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-31}{17} & & \\ & V = \left\{ \frac{-31}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x-6)& = & 13 \color{red}{+} (-4-4x) \\\Leftrightarrow & -5x-30& = &13-4-4x \\\Leftrightarrow & -5x \color{red}{-30} & = &9 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & -5x+4x& = &9+30 \\\Leftrightarrow & -x& = &39 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{39}{ \color{red}{-1} } \\\Leftrightarrow & x = -39 & & \\ & V = \left\{ -39 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x-6)& = & 14 \color{red}{+} (7+x) \\\Leftrightarrow & 5x-30& = &14+7+x \\\Leftrightarrow & 5x \color{red}{-30} & = &21 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 5x-x& = &21+30 \\\Leftrightarrow & 4x& = &51 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{51}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{51}{4} & & \\ & V = \left\{ \frac{51}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-5)& = & 9 \color{red}{-} (13+29x) \\\Leftrightarrow & 30x-30& = &9-13-29x \\\Leftrightarrow & 30x \color{red}{-30} & = &-4 \color{red}{-29x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+29x} & = &-4 \color{red}{-29x} \color{blue}{+29x} \color{blue}{+30} \\\Leftrightarrow & 30x+29x& = &-4+30 \\\Leftrightarrow & 59x& = &26 \\\Leftrightarrow & \frac{59x}{ \color{red}{59} }& = &\frac{26}{ \color{red}{59} } \\\Leftrightarrow & x = \frac{26}{59} & & \\ & V = \left\{ \frac{26}{59} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-1)& = & -5 \color{red}{+} (5+11x) \\\Leftrightarrow & -12x-3& = &-5+5+11x \\\Leftrightarrow & -12x \color{red}{-3} & = &0 \color{red}{+11x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-11x} & = &0 \color{red}{+11x} \color{blue}{-11x} \color{blue}{+3} \\\Leftrightarrow & -12x-11x& = &0+3 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+3)& = & 6 \color{red}{+} (12+5x) \\\Leftrightarrow & 12x+18& = &6+12+5x \\\Leftrightarrow & 12x \color{red}{+18} & = &18 \color{red}{+5x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 12x-5x& = &18-18 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-2)& = & 15 \color{red}{+} (14+x) \\\Leftrightarrow & -18x-6& = &15+14+x \\\Leftrightarrow & -18x \color{red}{-6} & = &29 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -18x-x& = &29+6 \\\Leftrightarrow & -19x& = &35 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{35}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-35}{19} & & \\ & V = \left\{ \frac{-35}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-7)& = & -5 \color{red}{+} (5-2x) \\\Leftrightarrow & -9x-21& = &-5+5-2x \\\Leftrightarrow & -9x \color{red}{-21} & = &0 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{+2x} & = &0 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+21} \\\Leftrightarrow & -9x+2x& = &0+21 \\\Leftrightarrow & -7x& = &21 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{21}{ \color{red}{-7} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x-4)& = & 4 \color{red}{+} (6+5x) \\\Leftrightarrow & 3x-12& = &4+6+5x \\\Leftrightarrow & 3x \color{red}{-12} & = &10 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 3x-5x& = &10+12 \\\Leftrightarrow & -2x& = &22 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{22}{ \color{red}{-2} } \\\Leftrightarrow & x = -11 & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-5)& = & 2 \color{red}{-} (-3-3x) \\\Leftrightarrow & -10x-10& = &2+3+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &5+10 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+6)& = & 9 \color{red}{-} (7-5x) \\\Leftrightarrow & -36x+36& = &9-7+5x \\\Leftrightarrow & -36x \color{red}{+36} & = &2 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & -36x-5x& = &2-36 \\\Leftrightarrow & -41x& = &-34 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-34}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{34}{41} & & \\ & V = \left\{ \frac{34}{41} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+7)& = & 3 \color{red}{-} (-9+4x) \\\Leftrightarrow & 15x+35& = &3+9-4x \\\Leftrightarrow & 15x \color{red}{+35} & = &12 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & 15x+4x& = &12-35 \\\Leftrightarrow & 19x& = &-23 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-23}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-23}{19} & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)