Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

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