Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-x } & = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &2x & = &12\\\Leftrightarrow & \color{red}{2}x & = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+9}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-7x } & = & -5 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-20x & = &-14\\\Leftrightarrow & \color{red}{-20}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-14}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-1}& = & -5 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+8x } & = & -5 \color{red}{ -8x }\color{blue}{+1+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+10}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-6x } & = & -2 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-15}& = & -10 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+9x } & = & -10 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &10x & = &5\\\Leftrightarrow & \color{red}{10}x & = &5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-21\\\Leftrightarrow & \color{red}{-13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & -15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-12x & = &-21\\\Leftrightarrow & \color{red}{-12}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+2}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+11x } & = & -6 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+4}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+2x } & = & -2 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &17x & = &-6\\\Leftrightarrow & \color{red}{17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)