Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{8})& = & 2x+\frac{7}{4} \\\Leftrightarrow & 15x+\frac{15}{8}& = & 2x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{+15} & = & \color{red}{16x} +14 \\\Leftrightarrow & 120x \color{red}{+15} \color{blue}{-15} \color{blue}{-16x} & = & \color{red}{16x} +14 \color{blue}{-16x} \color{blue}{-15} \\\Leftrightarrow & 120x-16x& = & 14-15 \\\Leftrightarrow & \color{red}{104} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{104} & & \\ & V = \left\{ \frac{-1}{104} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{175x} +15 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -315x-175x& = & 15+84 \\\Leftrightarrow & \color{red}{-490} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-490} & & \\\Leftrightarrow & x = \frac{-99}{490} & & \\ & V = \left\{ \frac{-99}{490} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{7})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x+\frac{20}{7}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x+ \frac{80}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{+80} & = & \color{red}{140x} +21 \\\Leftrightarrow & -336x \color{red}{+80} \color{blue}{-80} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{-80} \\\Leftrightarrow & -336x-140x& = & 21-80 \\\Leftrightarrow & \color{red}{-476} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-476} & & \\\Leftrightarrow & x = \frac{59}{476} & & \\ & V = \left\{ \frac{59}{476} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{+108} & = & \color{red}{315x} +20 \\\Leftrightarrow & -1350x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & -1350x-315x& = & 20-108 \\\Leftrightarrow & \color{red}{-1665} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-1665} & & \\\Leftrightarrow & x = \frac{88}{1665} & & \\ & V = \left\{ \frac{88}{1665} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{11})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -18x-\frac{24}{11}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-24} & = & \color{red}{55x} +10 \\\Leftrightarrow & -198x \color{red}{-24} \color{blue}{+24} \color{blue}{-55x} & = & \color{red}{55x} +10 \color{blue}{-55x} \color{blue}{+24} \\\Leftrightarrow & -198x-55x& = & 10+24 \\\Leftrightarrow & \color{red}{-253} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-253} & & \\\Leftrightarrow & x = \frac{-34}{253} & & \\ & V = \left\{ \frac{-34}{253} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{7})& = & -2x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+18} & = & \color{red}{-42x} +28 \\\Leftrightarrow & 315x \color{red}{+18} \color{blue}{-18} \color{blue}{+42x} & = & \color{red}{-42x} +28 \color{blue}{+42x} \color{blue}{-18} \\\Leftrightarrow & 315x+42x& = & 28-18 \\\Leftrightarrow & \color{red}{357} x& = & 10 \\\Leftrightarrow & x = \frac{10}{357} & & \\ & V = \left\{ \frac{10}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{2})& = & -4x+\frac{2}{9} \\\Leftrightarrow & 21x+\frac{21}{2}& = & -4x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{378}{ \color{blue}{18} }x+ \frac{189}{ \color{blue}{18} })& = & (\frac{-72}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 378x \color{red}{+189} & = & \color{red}{-72x} +4 \\\Leftrightarrow & 378x \color{red}{+189} \color{blue}{-189} \color{blue}{+72x} & = & \color{red}{-72x} +4 \color{blue}{+72x} \color{blue}{-189} \\\Leftrightarrow & 378x+72x& = & 4-189 \\\Leftrightarrow & \color{red}{450} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{450} & & \\\Leftrightarrow & x = \frac{-37}{90} & & \\ & V = \left\{ \frac{-37}{90} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{3})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{8}{3}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-24} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -54x \color{red}{-24} \color{blue}{+24} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+24} \\\Leftrightarrow & -54x+63x& = & 4+24 \\\Leftrightarrow & \color{red}{9} x& = & 28 \\\Leftrightarrow & x = \frac{28}{9} & & \\ & V = \left\{ \frac{28}{9} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{7})& = & 4x+\frac{9}{4} \\\Leftrightarrow & -25x+\frac{15}{7}& = & 4x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x+ \frac{60}{ \color{blue}{28} })& = & (\frac{112}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{+60} & = & \color{red}{112x} +63 \\\Leftrightarrow & -700x \color{red}{+60} \color{blue}{-60} \color{blue}{-112x} & = & \color{red}{112x} +63 \color{blue}{-112x} \color{blue}{-60} \\\Leftrightarrow & -700x-112x& = & 63-60 \\\Leftrightarrow & \color{red}{-812} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-812} & & \\\Leftrightarrow & x = \frac{-3}{812} & & \\ & V = \left\{ \frac{-3}{812} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{9}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{+36} & = & \color{red}{140x} +63 \\\Leftrightarrow & -336x \color{red}{+36} \color{blue}{-36} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{-36} \\\Leftrightarrow & -336x-140x& = & 63-36 \\\Leftrightarrow & \color{red}{-476} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-476} & & \\\Leftrightarrow & x = \frac{-27}{476} & & \\ & V = \left\{ \frac{-27}{476} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -10x+\frac{8}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+56} & = & \color{red}{539x} +44 \\\Leftrightarrow & -770x \color{red}{+56} \color{blue}{-56} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{-56} \\\Leftrightarrow & -770x-539x& = & 44-56 \\\Leftrightarrow & \color{red}{-1309} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-1309} & & \\\Leftrightarrow & x = \frac{12}{1309} & & \\ & V = \left\{ \frac{12}{1309} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{12}{11}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{-24} & = & \color{red}{-198x} +33 \\\Leftrightarrow & -176x \color{red}{-24} \color{blue}{+24} \color{blue}{+198x} & = & \color{red}{-198x} +33 \color{blue}{+198x} \color{blue}{+24} \\\Leftrightarrow & -176x+198x& = & 33+24 \\\Leftrightarrow & \color{red}{22} x& = & 57 \\\Leftrightarrow & x = \frac{57}{22} & & \\ & V = \left\{ \frac{57}{22} \right\} & \\\end{align}\)