Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-4}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4+7x } & = & 5 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &15x & = &9\\\Leftrightarrow & \color{red}{15}x & = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-11}& = & 13 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+14x } & = & 13 \color{red}{ -14x }\color{blue}{+11+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &29x & = &24\\\Leftrightarrow & \color{red}{29}x & = &24\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{24}{29} \\\Leftrightarrow & \color{green}{ x = \frac{24}{29} } & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+4}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-4x } & = & 1 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-8}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+9x } & = & -13 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &23x & = &-5\\\Leftrightarrow & \color{red}{23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x } & = & 14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-12x & = &24\\\Leftrightarrow & \color{red}{-12}x & = &24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{24}{-12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-16x & = &5\\\Leftrightarrow & \color{red}{-16}x & = &5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-15}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-13x } & = & 14 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-17x & = &29\\\Leftrightarrow & \color{red}{-17}x & = &29\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{29}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{17} } & & \\ & V = \left\{ \frac{-29}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+9}& = & -2 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-12x } & = & -2 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-9}& = & 4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+6x } & = & 4 \color{red}{ -6x }\color{blue}{+9+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &19x & = &13\\\Leftrightarrow & \color{red}{19}x & = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-3}& = & 6 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-2x } & = & 6 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)