Vgln. eerste graad (reeks 4)

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1. \(\frac{x}{3}-\frac{3}{16}=\frac{3}{2}x-6\)
2. \(\frac{x}{5}-\frac{3}{10}=\frac{3}{4}x+6\)
3. \(\frac{x}{5}+\frac{3}{13}=\frac{1}{4}x+3\)
4. \(\frac{x}{7}-\frac{5}{14}=\frac{-7}{4}x+6\)
5. \(\frac{x}{4}-\frac{3}{7}=\frac{-5}{3}x-2\)
6. \(\frac{x}{5}-\frac{3}{7}=\frac{3}{4}x-6\)
7. \(\frac{x}{3}-\frac{5}{11}=\frac{3}{2}x+6\)
8. \(\frac{x}{7}+\frac{5}{11}=\frac{7}{2}x+4\)
9. \(\frac{x}{3}-\frac{2}{11}=\frac{1}{2}x-5\)
10. \(\frac{x}{3}-\frac{5}{14}=\frac{-4}{5}x+8\)
11. \(\frac{x}{5}-\frac{2}{15}=\frac{1}{2}x+8\)
12. \(\frac{x}{5}+\frac{4}{13}=\frac{1}{4}x+6\)

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Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

Verbetersleutel

1. \(\text{48 is het kleinste gemene veelvoud van 3, 16 en 2} \\ \begin{align} & \frac{x}{3}-\frac{3}{16}& = & \frac{3}{2}x-6 \\\Leftrightarrow & \color{blue}{48.} (\frac{16x}{ \color{blue}{48} }- \frac{ 9 }{ \color{blue}{48} })& = & (\frac{72}{ \color{blue}{48} }x-\frac{288}{ \color{blue}{48} }) \color{blue}{.48} \\\Leftrightarrow & 16x-9& = & 72x-288 \\\Leftrightarrow & 16x \color{red}{-9} \color{blue}{+9} \color{blue}{-72x} & = & \color{red}{72x} -288 \color{blue}{-72x} \color{blue}{+9} \\\Leftrightarrow & -56x& = & -279 \\\Leftrightarrow & \frac{-56x}{ \color{red}{-56} }& = & \frac{-279}{-56} \\\Leftrightarrow & x = \frac{279}{56} & & \\ & V = \left\{ \frac{279}{56} \right\} & \\\end{align}\)
2. \(\text{20 is het kleinste gemene veelvoud van 5, 10 en 4} \\ \begin{align} & \frac{x}{5}-\frac{3}{10}& = & \frac{3}{4}x+6 \\\Leftrightarrow & \color{blue}{20.} (\frac{4x}{ \color{blue}{20} }- \frac{ 6 }{ \color{blue}{20} })& = & (\frac{15}{ \color{blue}{20} }x+\frac{120}{ \color{blue}{20} }) \color{blue}{.20} \\\Leftrightarrow & 4x-6& = & 15x+120 \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{-15x} & = & \color{red}{15x} +120 \color{blue}{-15x} \color{blue}{+6} \\\Leftrightarrow & -11x& = & 126 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = & \frac{126}{-11} \\\Leftrightarrow & x = \frac{-126}{11} & & \\ & V = \left\{ \frac{-126}{11} \right\} & \\\end{align}\)
3. \(\text{260 is het kleinste gemene veelvoud van 5, 13 en 4} \\ \begin{align} & \frac{x}{5}+\frac{3}{13}& = & \frac{1}{4}x+3 \\\Leftrightarrow & \color{blue}{260.} (\frac{52x}{ \color{blue}{260} }+ \frac{ 60 }{ \color{blue}{260} })& = & (\frac{65}{ \color{blue}{260} }x+\frac{780}{ \color{blue}{260} }) \color{blue}{.260} \\\Leftrightarrow & 52x+60& = & 65x+780 \\\Leftrightarrow & 52x \color{red}{+60} \color{blue}{-60} \color{blue}{-65x} & = & \color{red}{65x} +780 \color{blue}{-65x} \color{blue}{-60} \\\Leftrightarrow & -13x& = & 720 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = & \frac{720}{-13} \\\Leftrightarrow & x = \frac{-720}{13} & & \\ & V = \left\{ \frac{-720}{13} \right\} & \\\end{align}\)
4. \(\text{28 is het kleinste gemene veelvoud van 7, 14 en 4} \\ \begin{align} & \frac{x}{7}-\frac{5}{14}& = & \frac{-7}{4}x+6 \\\Leftrightarrow & \color{blue}{28.} (\frac{4x}{ \color{blue}{28} }- \frac{ 10 }{ \color{blue}{28} })& = & (\frac{-49}{ \color{blue}{28} }x+\frac{168}{ \color{blue}{28} }) \color{blue}{.28} \\\Leftrightarrow & 4x-10& = & -49x+168 \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +168 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & 53x& = & 178 \\\Leftrightarrow & \frac{53x}{ \color{red}{53} }& = & \frac{178}{53} \\\Leftrightarrow & x = \frac{178}{53} & & \\ & V = \left\{ \frac{178}{53} \right\} & \\\end{align}\)
5. \(\text{84 is het kleinste gemene veelvoud van 4, 7 en 3} \\ \begin{align} & \frac{x}{4}-\frac{3}{7}& = & \frac{-5}{3}x-2 \\\Leftrightarrow & \color{blue}{84.} (\frac{21x}{ \color{blue}{84} }- \frac{ 36 }{ \color{blue}{84} })& = & (\frac{-140}{ \color{blue}{84} }x-\frac{168}{ \color{blue}{84} }) \color{blue}{.84} \\\Leftrightarrow & 21x-36& = & -140x-168 \\\Leftrightarrow & 21x \color{red}{-36} \color{blue}{+36} \color{blue}{+140x} & = & \color{red}{-140x} -168 \color{blue}{+140x} \color{blue}{+36} \\\Leftrightarrow & 161x& = & -132 \\\Leftrightarrow & \frac{161x}{ \color{red}{161} }& = & \frac{-132}{161} \\\Leftrightarrow & x = \frac{-132}{161} & & \\ & V = \left\{ \frac{-132}{161} \right\} & \\\end{align}\)
6. \(\text{140 is het kleinste gemene veelvoud van 5, 7 en 4} \\ \begin{align} & \frac{x}{5}-\frac{3}{7}& = & \frac{3}{4}x-6 \\\Leftrightarrow & \color{blue}{140.} (\frac{28x}{ \color{blue}{140} }- \frac{ 60 }{ \color{blue}{140} })& = & (\frac{105}{ \color{blue}{140} }x-\frac{840}{ \color{blue}{140} }) \color{blue}{.140} \\\Leftrightarrow & 28x-60& = & 105x-840 \\\Leftrightarrow & 28x \color{red}{-60} \color{blue}{+60} \color{blue}{-105x} & = & \color{red}{105x} -840 \color{blue}{-105x} \color{blue}{+60} \\\Leftrightarrow & -77x& = & -780 \\\Leftrightarrow & \frac{-77x}{ \color{red}{-77} }& = & \frac{-780}{-77} \\\Leftrightarrow & x = \frac{780}{77} & & \\ & V = \left\{ \frac{780}{77} \right\} & \\\end{align}\)
7. \(\text{66 is het kleinste gemene veelvoud van 3, 11 en 2} \\ \begin{align} & \frac{x}{3}-\frac{5}{11}& = & \frac{3}{2}x+6 \\\Leftrightarrow & \color{blue}{66.} (\frac{22x}{ \color{blue}{66} }- \frac{ 30 }{ \color{blue}{66} })& = & (\frac{99}{ \color{blue}{66} }x+\frac{396}{ \color{blue}{66} }) \color{blue}{.66} \\\Leftrightarrow & 22x-30& = & 99x+396 \\\Leftrightarrow & 22x \color{red}{-30} \color{blue}{+30} \color{blue}{-99x} & = & \color{red}{99x} +396 \color{blue}{-99x} \color{blue}{+30} \\\Leftrightarrow & -77x& = & 426 \\\Leftrightarrow & \frac{-77x}{ \color{red}{-77} }& = & \frac{426}{-77} \\\Leftrightarrow & x = \frac{-426}{77} & & \\ & V = \left\{ \frac{-426}{77} \right\} & \\\end{align}\)
8. \(\text{154 is het kleinste gemene veelvoud van 7, 11 en 2} \\ \begin{align} & \frac{x}{7}+\frac{5}{11}& = & \frac{7}{2}x+4 \\\Leftrightarrow & \color{blue}{154.} (\frac{22x}{ \color{blue}{154} }+ \frac{ 70 }{ \color{blue}{154} })& = & (\frac{539}{ \color{blue}{154} }x+\frac{616}{ \color{blue}{154} }) \color{blue}{.154} \\\Leftrightarrow & 22x+70& = & 539x+616 \\\Leftrightarrow & 22x \color{red}{+70} \color{blue}{-70} \color{blue}{-539x} & = & \color{red}{539x} +616 \color{blue}{-539x} \color{blue}{-70} \\\Leftrightarrow & -517x& = & 546 \\\Leftrightarrow & \frac{-517x}{ \color{red}{-517} }& = & \frac{546}{-517} \\\Leftrightarrow & x = \frac{-546}{517} & & \\ & V = \left\{ \frac{-546}{517} \right\} & \\\end{align}\)
9. \(\text{66 is het kleinste gemene veelvoud van 3, 11 en 2} \\ \begin{align} & \frac{x}{3}-\frac{2}{11}& = & \frac{1}{2}x-5 \\\Leftrightarrow & \color{blue}{66.} (\frac{22x}{ \color{blue}{66} }- \frac{ 12 }{ \color{blue}{66} })& = & (\frac{33}{ \color{blue}{66} }x-\frac{330}{ \color{blue}{66} }) \color{blue}{.66} \\\Leftrightarrow & 22x-12& = & 33x-330 \\\Leftrightarrow & 22x \color{red}{-12} \color{blue}{+12} \color{blue}{-33x} & = & \color{red}{33x} -330 \color{blue}{-33x} \color{blue}{+12} \\\Leftrightarrow & -11x& = & -318 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = & \frac{-318}{-11} \\\Leftrightarrow & x = \frac{318}{11} & & \\ & V = \left\{ \frac{318}{11} \right\} & \\\end{align}\)
10. \(\text{210 is het kleinste gemene veelvoud van 3, 14 en 5} \\ \begin{align} & \frac{x}{3}-\frac{5}{14}& = & \frac{-4}{5}x+8 \\\Leftrightarrow & \color{blue}{210.} (\frac{70x}{ \color{blue}{210} }- \frac{ 75 }{ \color{blue}{210} })& = & (\frac{-168}{ \color{blue}{210} }x+\frac{1680}{ \color{blue}{210} }) \color{blue}{.210} \\\Leftrightarrow & 70x-75& = & -168x+1680 \\\Leftrightarrow & 70x \color{red}{-75} \color{blue}{+75} \color{blue}{+168x} & = & \color{red}{-168x} +1680 \color{blue}{+168x} \color{blue}{+75} \\\Leftrightarrow & 238x& = & 1755 \\\Leftrightarrow & \frac{238x}{ \color{red}{238} }& = & \frac{1755}{238} \\\Leftrightarrow & x = \frac{1755}{238} & & \\ & V = \left\{ \frac{1755}{238} \right\} & \\\end{align}\)
11. \(\text{30 is het kleinste gemene veelvoud van 5, 15 en 2} \\ \begin{align} & \frac{x}{5}-\frac{2}{15}& = & \frac{1}{2}x+8 \\\Leftrightarrow & \color{blue}{30.} (\frac{6x}{ \color{blue}{30} }- \frac{ 4 }{ \color{blue}{30} })& = & (\frac{15}{ \color{blue}{30} }x+\frac{240}{ \color{blue}{30} }) \color{blue}{.30} \\\Leftrightarrow & 6x-4& = & 15x+240 \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-15x} & = & \color{red}{15x} +240 \color{blue}{-15x} \color{blue}{+4} \\\Leftrightarrow & -9x& = & 244 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = & \frac{244}{-9} \\\Leftrightarrow & x = \frac{-244}{9} & & \\ & V = \left\{ \frac{-244}{9} \right\} & \\\end{align}\)
12. \(\text{260 is het kleinste gemene veelvoud van 5, 13 en 4} \\ \begin{align} & \frac{x}{5}+\frac{4}{13}& = & \frac{1}{4}x+6 \\\Leftrightarrow & \color{blue}{260.} (\frac{52x}{ \color{blue}{260} }+ \frac{ 80 }{ \color{blue}{260} })& = & (\frac{65}{ \color{blue}{260} }x+\frac{1560}{ \color{blue}{260} }) \color{blue}{.260} \\\Leftrightarrow & 52x+80& = & 65x+1560 \\\Leftrightarrow & 52x \color{red}{+80} \color{blue}{-80} \color{blue}{-65x} & = & \color{red}{65x} +1560 \color{blue}{-65x} \color{blue}{-80} \\\Leftrightarrow & -13x& = & 1480 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = & \frac{1480}{-13} \\\Leftrightarrow & x = \frac{-1480}{13} & & \\ & V = \left\{ \frac{-1480}{13} \right\} & \\\end{align}\)