Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x+6)& = & 10 \color{red}{-} (2+x) \\\Leftrightarrow & 30x+36& = &10-2-x \\\Leftrightarrow & 30x \color{red}{+36} & = &8 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &8-36 \\\Leftrightarrow & 31x& = &-28 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-28}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-28}{31} & & \\ & V = \left\{ \frac{-28}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x+5)& = & -1 \color{red}{-} (-14+x) \\\Leftrightarrow & 10x+25& = &-1+14-x \\\Leftrightarrow & 10x \color{red}{+25} & = &13 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 10x+x& = &13-25 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x-5)& = & -10 \color{red}{-} (8-2x) \\\Leftrightarrow & -15x-15& = &-10-8+2x \\\Leftrightarrow & -15x \color{red}{-15} & = &-18 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -15x-2x& = &-18+15 \\\Leftrightarrow & -17x& = &-3 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-3}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x-1)& = & 8 \color{red}{+} (1-4x) \\\Leftrightarrow & -9x-3& = &8+1-4x \\\Leftrightarrow & -9x \color{red}{-3} & = &9 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-3} \color{blue}{+3} \color{blue}{+4x} & = &9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+3} \\\Leftrightarrow & -9x+4x& = &9+3 \\\Leftrightarrow & -5x& = &12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+4)& = & 11 \color{red}{-} (-10+x) \\\Leftrightarrow & 20x+16& = &11+10-x \\\Leftrightarrow & 20x \color{red}{+16} & = &21 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 20x+x& = &21-16 \\\Leftrightarrow & 21x& = &5 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{5}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{5}{21} & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-3)& = & -13 \color{red}{-} (-7-5x) \\\Leftrightarrow & -36x-18& = &-13+7+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &-6 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &-6+18 \\\Leftrightarrow & -41x& = &12 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{12}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-12}{41} & & \\ & V = \left\{ \frac{-12}{41} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x+4)& = & 6 \color{red}{+} (-15-5x) \\\Leftrightarrow & -6x+8& = &6-15-5x \\\Leftrightarrow & -6x \color{red}{+8} & = &-9 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -6x+5x& = &-9-8 \\\Leftrightarrow & -x& = &-17 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-17}{ \color{red}{-1} } \\\Leftrightarrow & x = 17 & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+1)& = & -2 \color{red}{+} (-6-5x) \\\Leftrightarrow & 18x+3& = &-2-6-5x \\\Leftrightarrow & 18x \color{red}{+3} & = &-8 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & 18x+5x& = &-8-3 \\\Leftrightarrow & 23x& = &-11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x+1)& = & 14 \color{red}{-} (5+x) \\\Leftrightarrow & -20x+4& = &14-5-x \\\Leftrightarrow & -20x \color{red}{+4} & = &9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -20x+x& = &9-4 \\\Leftrightarrow & -19x& = &5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-5}{19} & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x-6)& = & 15 \color{red}{-} (14-2x) \\\Leftrightarrow & -15x-30& = &15-14+2x \\\Leftrightarrow & -15x \color{red}{-30} & = &1 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & -15x-2x& = &1+30 \\\Leftrightarrow & -17x& = &31 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{31}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-31}{17} & & \\ & V = \left\{ \frac{-31}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x+3)& = & 9 \color{red}{+} (-7+x) \\\Leftrightarrow & -8x+12& = &9-7+x \\\Leftrightarrow & -8x \color{red}{+12} & = &2 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -8x-x& = &2-12 \\\Leftrightarrow & -9x& = &-10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+7)& = & -4 \color{red}{+} (11+x) \\\Leftrightarrow & -10x+35& = &-4+11+x \\\Leftrightarrow & -10x \color{red}{+35} & = &7 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -10x-x& = &7-35 \\\Leftrightarrow & -11x& = &-28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)