Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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