Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x-4)& = & -14 \color{red}{-} (10+3x) \\\Leftrightarrow & -5x-20& = &-14-10-3x \\\Leftrightarrow & -5x \color{red}{-20} & = &-24 \color{red}{-3x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-24 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -5x+3x& = &-24+20 \\\Leftrightarrow & -2x& = &-4 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-4}{ \color{red}{-2} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x+2)& = & -12 \color{red}{-} (10+x) \\\Leftrightarrow & -30x+12& = &-12-10-x \\\Leftrightarrow & -30x \color{red}{+12} & = &-22 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -30x+x& = &-22-12 \\\Leftrightarrow & -29x& = &-34 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-34}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{34}{29} & & \\ & V = \left\{ \frac{34}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x+2)& = & -9 \color{red}{+} (-3+x) \\\Leftrightarrow & 4x+8& = &-9-3+x \\\Leftrightarrow & 4x \color{red}{+8} & = &-12 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 4x-x& = &-12-8 \\\Leftrightarrow & 3x& = &-20 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-20}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x-2)& = & -7 \color{red}{-} (2+x) \\\Leftrightarrow & 30x-10& = &-7-2-x \\\Leftrightarrow & 30x \color{red}{-10} & = &-9 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &-9+10 \\\Leftrightarrow & 31x& = &1 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{1}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{1}{31} & & \\ & V = \left\{ \frac{1}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-2)& = & 3 \color{red}{-} (6-5x) \\\Leftrightarrow & -8x-8& = &3-6+5x \\\Leftrightarrow & -8x \color{red}{-8} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & -8x-5x& = &-3+8 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-5)& = & -9 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x-20& = &-9+8-x \\\Leftrightarrow & -24x \color{red}{-20} & = &-1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -24x+x& = &-1+20 \\\Leftrightarrow & -23x& = &19 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{19}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-19}{23} & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x-6)& = & 7 \color{red}{+} (8+x) \\\Leftrightarrow & 30x-30& = &7+8+x \\\Leftrightarrow & 30x \color{red}{-30} & = &15 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &15+30 \\\Leftrightarrow & 29x& = &45 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{45}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{45}{29} & & \\ & V = \left\{ \frac{45}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+6)& = & -5 \color{red}{+} (7-3x) \\\Leftrightarrow & -16x+24& = &-5+7-3x \\\Leftrightarrow & -16x \color{red}{+24} & = &2 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -16x+3x& = &2-24 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+5)& = & 15 \color{red}{+} (-12+3x) \\\Leftrightarrow & -2x+10& = &15-12+3x \\\Leftrightarrow & -2x \color{red}{+10} & = &3 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -2x-3x& = &3-10 \\\Leftrightarrow & -5x& = &-7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-1)& = & -12 \color{red}{-} (5-5x) \\\Leftrightarrow & -8x-2& = &-12-5+5x \\\Leftrightarrow & -8x \color{red}{-2} & = &-17 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & -8x-5x& = &-17+2 \\\Leftrightarrow & -13x& = &-15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x+3)& = & 15 \color{red}{-} (13+x) \\\Leftrightarrow & -30x+15& = &15-13-x \\\Leftrightarrow & -30x \color{red}{+15} & = &2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &2-15 \\\Leftrightarrow & -29x& = &-13 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-13}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{13}{29} & & \\ & V = \left\{ \frac{13}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+7)& = & -5 \color{red}{-} (2-3x) \\\Leftrightarrow & 4x+28& = &-5-2+3x \\\Leftrightarrow & 4x \color{red}{+28} & = &-7 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & 4x-3x& = &-7-28 \\\Leftrightarrow & x& = &-35 \\ & V = \left\{ -35 \right\} & \\\end{align}\)