Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{9})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-8} & = & \color{red}{-63x} +24 \\\Leftrightarrow & -54x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +24 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -54x+63x& = & 24+8 \\\Leftrightarrow & \color{red}{9} x& = & 32 \\\Leftrightarrow & x = \frac{32}{9} & & \\ & V = \left\{ \frac{32}{9} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 10x-\frac{4}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-44} & = & \color{red}{-385x} +10 \\\Leftrightarrow & 550x \color{red}{-44} \color{blue}{+44} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+44} \\\Leftrightarrow & 550x+385x& = & 10+44 \\\Leftrightarrow & \color{red}{935} x& = & 54 \\\Leftrightarrow & x = \frac{54}{935} & & \\ & V = \left\{ \frac{54}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{12})& = & -4x+\frac{10}{11} \\\Leftrightarrow & 21x-\frac{35}{12}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2772}{ \color{blue}{132} }x- \frac{385}{ \color{blue}{132} })& = & (\frac{-528}{ \color{blue}{132} }x+ \frac{120}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2772x \color{red}{-385} & = & \color{red}{-528x} +120 \\\Leftrightarrow & 2772x \color{red}{-385} \color{blue}{+385} \color{blue}{+528x} & = & \color{red}{-528x} +120 \color{blue}{+528x} \color{blue}{+385} \\\Leftrightarrow & 2772x+528x& = & 120+385 \\\Leftrightarrow & \color{red}{3300} x& = & 505 \\\Leftrightarrow & x = \frac{505}{3300} & & \\\Leftrightarrow & x = \frac{101}{660} & & \\ & V = \left\{ \frac{101}{660} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{20}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-60} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -210x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & -210x+147x& = & 14+60 \\\Leftrightarrow & \color{red}{-63} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-63} & & \\\Leftrightarrow & x = \frac{-74}{63} & & \\ & V = \left\{ \frac{-74}{63} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{3})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 15x+\frac{25}{3}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{100}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+100} & = & \color{red}{-84x} +27 \\\Leftrightarrow & 180x \color{red}{+100} \color{blue}{-100} \color{blue}{+84x} & = & \color{red}{-84x} +27 \color{blue}{+84x} \color{blue}{-100} \\\Leftrightarrow & 180x+84x& = & 27-100 \\\Leftrightarrow & \color{red}{264} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{264} & & \\ & V = \left\{ \frac{-73}{264} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+12} & = & \color{red}{-70x} +49 \\\Leftrightarrow & 168x \color{red}{+12} \color{blue}{-12} \color{blue}{+70x} & = & \color{red}{-70x} +49 \color{blue}{+70x} \color{blue}{-12} \\\Leftrightarrow & 168x+70x& = & 49-12 \\\Leftrightarrow & \color{red}{238} x& = & 37 \\\Leftrightarrow & x = \frac{37}{238} & & \\ & V = \left\{ \frac{37}{238} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+66} & = & \color{red}{693x} +42 \\\Leftrightarrow & -616x \color{red}{+66} \color{blue}{-66} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{-66} \\\Leftrightarrow & -616x-693x& = & 42-66 \\\Leftrightarrow & \color{red}{-1309} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-1309} & & \\\Leftrightarrow & x = \frac{24}{1309} & & \\ & V = \left\{ \frac{24}{1309} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -16x+\frac{12}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{+84} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -1232x \color{red}{+84} \color{blue}{-84} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-84} \\\Leftrightarrow & -1232x+539x& = & 110-84 \\\Leftrightarrow & \color{red}{-693} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-693} & & \\\Leftrightarrow & x = \frac{-26}{693} & & \\ & V = \left\{ \frac{-26}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -9x+\frac{6}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{+18} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -135x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -135x+105x& = & 40-18 \\\Leftrightarrow & \color{red}{-30} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-30} & & \\\Leftrightarrow & x = \frac{-11}{15} & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & -9x+\frac{3}{4} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x- \frac{64}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{-64} & = & \color{red}{-252x} +21 \\\Leftrightarrow & 224x \color{red}{-64} \color{blue}{+64} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{+64} \\\Leftrightarrow & 224x+252x& = & 21+64 \\\Leftrightarrow & \color{red}{476} x& = & 85 \\\Leftrightarrow & x = \frac{85}{476} & & \\\Leftrightarrow & x = \frac{5}{28} & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{9})& = & -9x+\frac{3}{11} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{27}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-88} & = & \color{red}{-891x} +27 \\\Leftrightarrow & -792x \color{red}{-88} \color{blue}{+88} \color{blue}{+891x} & = & \color{red}{-891x} +27 \color{blue}{+891x} \color{blue}{+88} \\\Leftrightarrow & -792x+891x& = & 27+88 \\\Leftrightarrow & \color{red}{99} x& = & 115 \\\Leftrightarrow & x = \frac{115}{99} & & \\ & V = \left\{ \frac{115}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-160}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -160x \color{red}{-24} & = & \color{red}{70x} +7 \\\Leftrightarrow & -160x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +7 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & -160x-70x& = & 7+24 \\\Leftrightarrow & \color{red}{-230} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-230} & & \\\Leftrightarrow & x = \frac{-31}{230} & & \\ & V = \left\{ \frac{-31}{230} \right\} & \\\end{align}\)