Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x-5)& = & -12 \color{red}{+} (12-5x) \\\Leftrightarrow & 18x-15& = &-12+12-5x \\\Leftrightarrow & 18x \color{red}{-15} & = &0 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 18x+5x& = &0+15 \\\Leftrightarrow & 23x& = &15 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{15}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x-5)& = & 10 \color{red}{+} (-11-5x) \\\Leftrightarrow & -6x-30& = &10-11-5x \\\Leftrightarrow & -6x \color{red}{-30} & = &-1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -6x+5x& = &-1+30 \\\Leftrightarrow & -x& = &29 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{29}{ \color{red}{-1} } \\\Leftrightarrow & x = -29 & & \\ & V = \left\{ -29 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-3x-1)& = & -15 \color{red}{+} (8+x) \\\Leftrightarrow & -6x-2& = &-15+8+x \\\Leftrightarrow & -6x \color{red}{-2} & = &-7 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -6x-x& = &-7+2 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+7)& = & -7 \color{red}{-} (13+x) \\\Leftrightarrow & 2x+14& = &-7-13-x \\\Leftrightarrow & 2x \color{red}{+14} & = &-20 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 2x+x& = &-20-14 \\\Leftrightarrow & 3x& = &-34 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-34}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-34}{3} & & \\ & V = \left\{ \frac{-34}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x+2)& = & 3 \color{red}{+} (-3+x) \\\Leftrightarrow & -10x+10& = &3-3+x \\\Leftrightarrow & -10x \color{red}{+10} & = &0 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -10x-x& = &0-10 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x+7)& = & -15 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x+42& = &-15+4-x \\\Leftrightarrow & -12x \color{red}{+42} & = &-11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &-11-42 \\\Leftrightarrow & -11x& = &-53 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-53}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{53}{11} & & \\ & V = \left\{ \frac{53}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-x-1)& = & 3 \color{red}{-} (7-5x) \\\Leftrightarrow & -6x-6& = &3-7+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &-4 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &-4+6 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+2)& = & 5 \color{red}{+} (10+x) \\\Leftrightarrow & 24x+12& = &5+10+x \\\Leftrightarrow & 24x \color{red}{+12} & = &15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &15-12 \\\Leftrightarrow & 23x& = &3 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{3}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x+3)& = & -13 \color{red}{-} (10+x) \\\Leftrightarrow & -12x+12& = &-13-10-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-23 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-23-12 \\\Leftrightarrow & -11x& = &-35 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-35}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{35}{11} & & \\ & V = \left\{ \frac{35}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x+6)& = & -1 \color{red}{-} (10-5x) \\\Leftrightarrow & -18x+36& = &-1-10+5x \\\Leftrightarrow & -18x \color{red}{+36} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & -18x-5x& = &-11-36 \\\Leftrightarrow & -23x& = &-47 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-47}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{47}{23} & & \\ & V = \left\{ \frac{47}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-6)& = & -8 \color{red}{-} (-9+x) \\\Leftrightarrow & 6x-12& = &-8+9-x \\\Leftrightarrow & 6x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &1+12 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-3)& = & 3 \color{red}{-} (5+x) \\\Leftrightarrow & -4x-6& = &3-5-x \\\Leftrightarrow & -4x \color{red}{-6} & = &-2 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -4x+x& = &-2+6 \\\Leftrightarrow & -3x& = &4 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{4}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)