Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x+4)& = & -13 \color{red}{-} (15+x) \\\Leftrightarrow & 24x+24& = &-13-15-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-28 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-28-24 \\\Leftrightarrow & 25x& = &-52 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-52}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-52}{25} & & \\ & V = \left\{ \frac{-52}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x+2)& = & -1 \color{red}{+} (14-3x) \\\Leftrightarrow & 10x+4& = &-1+14-3x \\\Leftrightarrow & 10x \color{red}{+4} & = &13 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 10x+3x& = &13-4 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x+7)& = & -12 \color{red}{+} (2-2x) \\\Leftrightarrow & -15x+35& = &-12+2-2x \\\Leftrightarrow & -15x \color{red}{+35} & = &-10 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &-10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & -15x+2x& = &-10-35 \\\Leftrightarrow & -13x& = &-45 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-45}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{45}{13} & & \\ & V = \left\{ \frac{45}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x+2)& = & -11 \color{red}{-} (1-5x) \\\Leftrightarrow & -6x+12& = &-11-1+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-12 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &-12-12 \\\Leftrightarrow & -11x& = &-24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{24}{11} & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-3)& = & -11 \color{red}{-} (-8+x) \\\Leftrightarrow & -18x-18& = &-11+8-x \\\Leftrightarrow & -18x \color{red}{-18} & = &-3 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -18x+x& = &-3+18 \\\Leftrightarrow & -17x& = &15 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{15}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-15}{17} & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x-4)& = & -3 \color{red}{-} (-7-5x) \\\Leftrightarrow & 16x-16& = &-3+7+5x \\\Leftrightarrow & 16x \color{red}{-16} & = &4 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+16} \\\Leftrightarrow & 16x-5x& = &4+16 \\\Leftrightarrow & 11x& = &20 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{20}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (4x-3)& = & -8 \color{red}{+} (4+x) \\\Leftrightarrow & 16x-12& = &-8+4+x \\\Leftrightarrow & 16x \color{red}{-12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 16x-x& = &-4+12 \\\Leftrightarrow & 15x& = &8 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{8}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{8}{15} & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x-2)& = & 9 \color{red}{+} (6+x) \\\Leftrightarrow & 30x-10& = &9+6+x \\\Leftrightarrow & 30x \color{red}{-10} & = &15 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 30x-x& = &15+10 \\\Leftrightarrow & 29x& = &25 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{25}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{25}{29} & & \\ & V = \left\{ \frac{25}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x+1)& = & -15 \color{red}{-} (10+x) \\\Leftrightarrow & -6x+6& = &-15-10-x \\\Leftrightarrow & -6x \color{red}{+6} & = &-25 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -6x+x& = &-25-6 \\\Leftrightarrow & -5x& = &-31 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-31}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{31}{5} & & \\ & V = \left\{ \frac{31}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x+3)& = & 3 \color{red}{+} (7-2x) \\\Leftrightarrow & -15x+15& = &3+7-2x \\\Leftrightarrow & -15x \color{red}{+15} & = &10 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & -15x+2x& = &10-15 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+7)& = & -5 \color{red}{+} (-4-3x) \\\Leftrightarrow & -4x+14& = &-5-4-3x \\\Leftrightarrow & -4x \color{red}{+14} & = &-9 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -4x+3x& = &-9-14 \\\Leftrightarrow & -x& = &-23 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-23}{ \color{red}{-1} } \\\Leftrightarrow & x = 23 & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x-5)& = & -14 \color{red}{-} (4-5x) \\\Leftrightarrow & -18x-30& = &-14-4+5x \\\Leftrightarrow & -18x \color{red}{-30} & = &-18 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -18x-5x& = &-18+30 \\\Leftrightarrow & -23x& = &12 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{12}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-12}{23} & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)