Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-3x-6)& = & 1 \color{red}{-} (-9+x) \\\Leftrightarrow & -12x-24& = &1+9-x \\\Leftrightarrow & -12x \color{red}{-24} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &10+24 \\\Leftrightarrow & -11x& = &34 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{34}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-34}{11} & & \\ & V = \left\{ \frac{-34}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x-4)& = & 13 \color{red}{+} (12+x) \\\Leftrightarrow & -36x-24& = &13+12+x \\\Leftrightarrow & -36x \color{red}{-24} & = &25 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -36x-x& = &25+24 \\\Leftrightarrow & -37x& = &49 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{49}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-49}{37} & & \\ & V = \left\{ \frac{-49}{37} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-1)& = & 8 \color{red}{-} (12+x) \\\Leftrightarrow & 12x-2& = &8-12-x \\\Leftrightarrow & 12x \color{red}{-2} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 12x+x& = &-4+2 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x-4)& = & 5 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x-16& = &5+5-x \\\Leftrightarrow & -12x \color{red}{-16} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -12x+x& = &10+16 \\\Leftrightarrow & -11x& = &26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-1)& = & -11 \color{red}{+} (-3-5x) \\\Leftrightarrow & -18x-3& = &-11-3-5x \\\Leftrightarrow & -18x \color{red}{-3} & = &-14 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -18x+5x& = &-14+3 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x+4)& = & -6 \color{red}{-} (-9+x) \\\Leftrightarrow & -12x+12& = &-6+9-x \\\Leftrightarrow & -12x \color{red}{+12} & = &3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &3-12 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-5)& = & -1 \color{red}{+} (1+x) \\\Leftrightarrow & -9x-15& = &-1+1+x \\\Leftrightarrow & -9x \color{red}{-15} & = &0 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -9x-x& = &0+15 \\\Leftrightarrow & -10x& = &15 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{15}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x+4)& = & 3 \color{red}{+} (8+x) \\\Leftrightarrow & 24x+16& = &3+8+x \\\Leftrightarrow & 24x \color{red}{+16} & = &11 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 24x-x& = &11-16 \\\Leftrightarrow & 23x& = &-5 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-5}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-5}{23} & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x-6)& = & 14 \color{red}{-} (10+x) \\\Leftrightarrow & -8x-24& = &14-10-x \\\Leftrightarrow & -8x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -8x+x& = &4+24 \\\Leftrightarrow & -7x& = &28 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{28}{ \color{red}{-7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x+7)& = & -7 \color{red}{+} (-13+x) \\\Leftrightarrow & -18x+42& = &-7-13+x \\\Leftrightarrow & -18x \color{red}{+42} & = &-20 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -18x-x& = &-20-42 \\\Leftrightarrow & -19x& = &-62 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-62}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{62}{19} & & \\ & V = \left\{ \frac{62}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-2x+4)& = & 5 \color{red}{-} (12-3x) \\\Leftrightarrow & -10x+20& = &5-12+3x \\\Leftrightarrow & -10x \color{red}{+20} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -10x-3x& = &-7-20 \\\Leftrightarrow & -13x& = &-27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x-7)& = & -5 \color{red}{-} (6+4x) \\\Leftrightarrow & 15x-35& = &-5-6-4x \\\Leftrightarrow & 15x \color{red}{-35} & = &-11 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+35} \\\Leftrightarrow & 15x+4x& = &-11+35 \\\Leftrightarrow & 19x& = &24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{24}{19} & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)