Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x+1)& = & 15 \color{red}{+} (-10+x) \\\Leftrightarrow & 12x+3& = &15-10+x \\\Leftrightarrow & 12x \color{red}{+3} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 12x-x& = &5-3 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x-3)& = & -9 \color{red}{-} (-10+x) \\\Leftrightarrow & -3x-9& = &-9+10-x \\\Leftrightarrow & -3x \color{red}{-9} & = &1 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -3x+x& = &1+9 \\\Leftrightarrow & -2x& = &10 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{10}{ \color{red}{-2} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-6x-6)& = & -4 \color{red}{+} (12+x) \\\Leftrightarrow & -36x-36& = &-4+12+x \\\Leftrightarrow & -36x \color{red}{-36} & = &8 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -36x-x& = &8+36 \\\Leftrightarrow & -37x& = &44 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{44}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-44}{37} & & \\ & V = \left\{ \frac{-44}{37} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x-7)& = & 13 \color{red}{-} (1+x) \\\Leftrightarrow & -9x-21& = &13-1-x \\\Leftrightarrow & -9x \color{red}{-21} & = &12 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -9x+x& = &12+21 \\\Leftrightarrow & -8x& = &33 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{33}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-33}{8} & & \\ & V = \left\{ \frac{-33}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x+7)& = & -10 \color{red}{+} (9+x) \\\Leftrightarrow & 6x+14& = &-10+9+x \\\Leftrightarrow & 6x \color{red}{+14} & = &-1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 6x-x& = &-1-14 \\\Leftrightarrow & 5x& = &-15 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-15}{ \color{red}{5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x-1)& = & -13 \color{red}{-} (7+3x) \\\Leftrightarrow & -20x-5& = &-13-7-3x \\\Leftrightarrow & -20x \color{red}{-5} & = &-20 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &-20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & -20x+3x& = &-20+5 \\\Leftrightarrow & -17x& = &-15 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-15}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{15}{17} & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x+5)& = & -9 \color{red}{-} (-3+x) \\\Leftrightarrow & -25x+25& = &-9+3-x \\\Leftrightarrow & -25x \color{red}{+25} & = &-6 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -25x+x& = &-6-25 \\\Leftrightarrow & -24x& = &-31 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{-31}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{31}{24} & & \\ & V = \left\{ \frac{31}{24} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x-7)& = & 13 \color{red}{+} (13+x) \\\Leftrightarrow & 16x-28& = &13+13+x \\\Leftrightarrow & 16x \color{red}{-28} & = &26 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 16x-x& = &26+28 \\\Leftrightarrow & 15x& = &54 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{54}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x+6)& = & -8 \color{red}{-} (13+x) \\\Leftrightarrow & -12x+24& = &-8-13-x \\\Leftrightarrow & -12x \color{red}{+24} & = &-21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -12x+x& = &-21-24 \\\Leftrightarrow & -11x& = &-45 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-45}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{45}{11} & & \\ & V = \left\{ \frac{45}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x+6)& = & 13 \color{red}{-} (15+x) \\\Leftrightarrow & 24x+36& = &13-15-x \\\Leftrightarrow & 24x \color{red}{+36} & = &-2 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 24x+x& = &-2-36 \\\Leftrightarrow & 25x& = &-38 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-38}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-38}{25} & & \\ & V = \left\{ \frac{-38}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-2)& = & 2 \color{red}{+} (-1+x) \\\Leftrightarrow & 20x-10& = &2-1+x \\\Leftrightarrow & 20x \color{red}{-10} & = &1 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &1+10 \\\Leftrightarrow & 19x& = &11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x+1)& = & 11 \color{red}{+} (11+x) \\\Leftrightarrow & 12x+2& = &11+11+x \\\Leftrightarrow & 12x \color{red}{+2} & = &22 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 12x-x& = &22-2 \\\Leftrightarrow & 11x& = &20 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{20}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)