Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+12}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-x } & = & -13 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-25\\\Leftrightarrow & \color{red}{-16}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-25}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{25}{16} } & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & 4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+5}& = & 4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5+6x } & = & 4 \color{red}{ -6x }\color{blue}{-5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+9}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+7x } & = & -2 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+3}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-7x } & = & 4 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-1}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1-3x } & = & -9 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &2x & = &-8\\\Leftrightarrow & \color{red}{2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-8}{2} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+1}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-8x } & = & 15 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &-23x & = &14\\\Leftrightarrow & \color{red}{-23}x & = &14\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{14}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{23} } & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+3}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-7x } & = & 6 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-5}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-8x } & = & 13 \color{red}{ +8x }\color{blue}{+5-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-9x & = &18\\\Leftrightarrow & \color{red}{-9}x & = &18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{18}{-9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-9\\\Leftrightarrow & \color{red}{-9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+10}& = & 2 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+4x } & = & 2 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)