Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x-1)& = & -7 \color{red}{-} (6-2x) \\\Leftrightarrow & -15x-3& = &-7-6+2x \\\Leftrightarrow & -15x \color{red}{-3} & = &-13 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &-13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & -15x-2x& = &-13+3 \\\Leftrightarrow & -17x& = &-10 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-10}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (6x-5)& = & -1 \color{red}{-} (6+x) \\\Leftrightarrow & 24x-20& = &-1-6-x \\\Leftrightarrow & 24x \color{red}{-20} & = &-7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 24x+x& = &-7+20 \\\Leftrightarrow & 25x& = &13 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{13}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{13}{25} & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x+7)& = & -15 \color{red}{+} (-10+x) \\\Leftrightarrow & -12x+28& = &-15-10+x \\\Leftrightarrow & -12x \color{red}{+28} & = &-25 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -12x-x& = &-25-28 \\\Leftrightarrow & -13x& = &-53 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-53}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{53}{13} & & \\ & V = \left\{ \frac{53}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-5x-4)& = & 14 \color{red}{-} (15+x) \\\Leftrightarrow & -10x-8& = &14-15-x \\\Leftrightarrow & -10x \color{red}{-8} & = &-1 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -10x+x& = &-1+8 \\\Leftrightarrow & -9x& = &7 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{7}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-7}{9} & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-3)& = & 14 \color{red}{-} (-1+x) \\\Leftrightarrow & 30x-18& = &14+1-x \\\Leftrightarrow & 30x \color{red}{-18} & = &15 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &15+18 \\\Leftrightarrow & 31x& = &33 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{33}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{33}{31} & & \\ & V = \left\{ \frac{33}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-6)& = & -13 \color{red}{-} (-8+x) \\\Leftrightarrow & -6x-36& = &-13+8-x \\\Leftrightarrow & -6x \color{red}{-36} & = &-5 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -6x+x& = &-5+36 \\\Leftrightarrow & -5x& = &31 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{31}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-31}{5} & & \\ & V = \left\{ \frac{-31}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x+5)& = & -10 \color{red}{+} (-4+x) \\\Leftrightarrow & 8x+10& = &-10-4+x \\\Leftrightarrow & 8x \color{red}{+10} & = &-14 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 8x-x& = &-14-10 \\\Leftrightarrow & 7x& = &-24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+5)& = & 15 \color{red}{-} (10+x) \\\Leftrightarrow & 2x+10& = &15-10-x \\\Leftrightarrow & 2x \color{red}{+10} & = &5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 2x+x& = &5-10 \\\Leftrightarrow & 3x& = &-5 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-5}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x-1)& = & 2 \color{red}{+} (-13+2x) \\\Leftrightarrow & 15x-3& = &2-13+2x \\\Leftrightarrow & 15x \color{red}{-3} & = &-11 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &-11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & 15x-2x& = &-11+3 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x+5)& = & -4 \color{red}{+} (15+3x) \\\Leftrightarrow & -4x+10& = &-4+15+3x \\\Leftrightarrow & -4x \color{red}{+10} & = &11 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -4x-3x& = &11-10 \\\Leftrightarrow & -7x& = &1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x+5)& = & 14 \color{red}{+} (-12+2x) \\\Leftrightarrow & -15x+15& = &14-12+2x \\\Leftrightarrow & -15x \color{red}{+15} & = &2 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -15x-2x& = &2-15 \\\Leftrightarrow & -17x& = &-13 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-13}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{13}{17} & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-4)& = & 3 \color{red}{+} (9-3x) \\\Leftrightarrow & -4x-8& = &3+9-3x \\\Leftrightarrow & -4x \color{red}{-8} & = &12 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -4x+3x& = &12+8 \\\Leftrightarrow & -x& = &20 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{20}{ \color{red}{-1} } \\\Leftrightarrow & x = -20 & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)