Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+6)& = & 1 \color{red}{+} (-15+x) \\\Leftrightarrow & 25x+30& = &1-15+x \\\Leftrightarrow & 25x \color{red}{+30} & = &-14 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 25x-x& = &-14-30 \\\Leftrightarrow & 24x& = &-44 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-44}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-11}{6} & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x+2)& = & -7 \color{red}{-} (8-3x) \\\Leftrightarrow & 10x+10& = &-7-8+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-15 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &-15-10 \\\Leftrightarrow & 7x& = &-25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x-4)& = & -3 \color{red}{+} (8+x) \\\Leftrightarrow & -24x-16& = &-3+8+x \\\Leftrightarrow & -24x \color{red}{-16} & = &5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -24x-x& = &5+16 \\\Leftrightarrow & -25x& = &21 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{21}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-21}{25} & & \\ & V = \left\{ \frac{-21}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-6)& = & 6 \color{red}{+} (-6+x) \\\Leftrightarrow & -6x-12& = &6-6+x \\\Leftrightarrow & -6x \color{red}{-12} & = &0 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -6x-x& = &0+12 \\\Leftrightarrow & -7x& = &12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+3)& = & -9 \color{red}{-} (4+x) \\\Leftrightarrow & -24x+12& = &-9-4-x \\\Leftrightarrow & -24x \color{red}{+12} & = &-13 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &-13-12 \\\Leftrightarrow & -23x& = &-25 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-25}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{25}{23} & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-6)& = & 14 \color{red}{+} (12+x) \\\Leftrightarrow & -30x-30& = &14+12+x \\\Leftrightarrow & -30x \color{red}{-30} & = &26 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &26+30 \\\Leftrightarrow & -31x& = &56 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{56}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-56}{31} & & \\ & V = \left\{ \frac{-56}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x+2)& = & -2 \color{red}{-} (-6+3x) \\\Leftrightarrow & -4x+8& = &-2+6-3x \\\Leftrightarrow & -4x \color{red}{+8} & = &4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -4x+3x& = &4-8 \\\Leftrightarrow & -x& = &-4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-4}{ \color{red}{-1} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x-6)& = & -3 \color{red}{+} (-3+x) \\\Leftrightarrow & 6x-12& = &-3-3+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-6+12 \\\Leftrightarrow & 5x& = &6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x+2)& = & 13 \color{red}{-} (-2-5x) \\\Leftrightarrow & 36x+12& = &13+2+5x \\\Leftrightarrow & 36x \color{red}{+12} & = &15 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 36x-5x& = &15-12 \\\Leftrightarrow & 31x& = &3 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{3}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{3}{31} & & \\ & V = \left\{ \frac{3}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-5)& = & 2 \color{red}{+} (12+x) \\\Leftrightarrow & 24x-20& = &2+12+x \\\Leftrightarrow & 24x \color{red}{-20} & = &14 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 24x-x& = &14+20 \\\Leftrightarrow & 23x& = &34 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{34}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{34}{23} & & \\ & V = \left\{ \frac{34}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x+1)& = & 8 \color{red}{-} (10+x) \\\Leftrightarrow & -15x+3& = &8-10-x \\\Leftrightarrow & -15x \color{red}{+3} & = &-2 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -15x+x& = &-2-3 \\\Leftrightarrow & -14x& = &-5 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-5}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{5}{14} & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x-6)& = & 13 \color{red}{-} (-15-5x) \\\Leftrightarrow & -18x-36& = &13+15+5x \\\Leftrightarrow & -18x \color{red}{-36} & = &28 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &28 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -18x-5x& = &28+36 \\\Leftrightarrow & -23x& = &64 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{64}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-64}{23} & & \\ & V = \left\{ \frac{-64}{23} \right\} & \\\end{align}\)