Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x+7)& = & 13 \color{red}{+} (3+x) \\\Leftrightarrow & -36x+42& = &13+3+x \\\Leftrightarrow & -36x \color{red}{+42} & = &16 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -36x-x& = &16-42 \\\Leftrightarrow & -37x& = &-26 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-26}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{26}{37} & & \\ & V = \left\{ \frac{26}{37} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x-3)& = & -8 \color{red}{-} (11+x) \\\Leftrightarrow & -12x-9& = &-8-11-x \\\Leftrightarrow & -12x \color{red}{-9} & = &-19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -12x+x& = &-19+9 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x-5)& = & -13 \color{red}{-} (-7+x) \\\Leftrightarrow & 6x-30& = &-13+7-x \\\Leftrightarrow & 6x \color{red}{-30} & = &-6 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 6x+x& = &-6+30 \\\Leftrightarrow & 7x& = &24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{24}{7} & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-3)& = & -4 \color{red}{+} (-12-4x) \\\Leftrightarrow & -25x-15& = &-4-12-4x \\\Leftrightarrow & -25x \color{red}{-15} & = &-16 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-16 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -25x+4x& = &-16+15 \\\Leftrightarrow & -21x& = &-1 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-1}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{1}{21} & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-7)& = & 13 \color{red}{-} (-4-5x) \\\Leftrightarrow & 16x-28& = &13+4+5x \\\Leftrightarrow & 16x \color{red}{-28} & = &17 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-28} \color{blue}{+28} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+28} \\\Leftrightarrow & 16x-5x& = &17+28 \\\Leftrightarrow & 11x& = &45 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{45}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{45}{11} & & \\ & V = \left\{ \frac{45}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-5)& = & 14 \color{red}{-} (1+2x) \\\Leftrightarrow & -25x-25& = &14-1-2x \\\Leftrightarrow & -25x \color{red}{-25} & = &13 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & -25x+2x& = &13+25 \\\Leftrightarrow & -23x& = &38 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{38}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-38}{23} & & \\ & V = \left\{ \frac{-38}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x-7)& = & 12 \color{red}{+} (9-3x) \\\Leftrightarrow & 4x-28& = &12+9-3x \\\Leftrightarrow & 4x \color{red}{-28} & = &21 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & 4x+3x& = &21+28 \\\Leftrightarrow & 7x& = &49 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{49}{ \color{red}{7} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+4)& = & 10 \color{red}{-} (-13+x) \\\Leftrightarrow & 18x+12& = &10+13-x \\\Leftrightarrow & 18x \color{red}{+12} & = &23 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &23-12 \\\Leftrightarrow & 19x& = &11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+6)& = & 6 \color{red}{+} (14+2x) \\\Leftrightarrow & 3x+18& = &6+14+2x \\\Leftrightarrow & 3x \color{red}{+18} & = &20 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &20 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & 3x-2x& = &20-18 \\\Leftrightarrow & x& = &2 \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x-4)& = & -4 \color{red}{+} (2-2x) \\\Leftrightarrow & -15x-20& = &-4+2-2x \\\Leftrightarrow & -15x \color{red}{-20} & = &-2 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & -15x+2x& = &-2+20 \\\Leftrightarrow & -13x& = &18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-x-2)& = & 3 \color{red}{+} (-1+x) \\\Leftrightarrow & -2x-4& = &3-1+x \\\Leftrightarrow & -2x \color{red}{-4} & = &2 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -2x-x& = &2+4 \\\Leftrightarrow & -3x& = &6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{6}{ \color{red}{-3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (5x+7)& = & 14 \color{red}{-} (-4-3x) \\\Leftrightarrow & 10x+14& = &14+4+3x \\\Leftrightarrow & 10x \color{red}{+14} & = &18 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 10x-3x& = &18-14 \\\Leftrightarrow & 7x& = &4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)