Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -25x-\frac{15}{4}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{-105} & = & \color{red}{196x} +16 \\\Leftrightarrow & -700x \color{red}{-105} \color{blue}{+105} \color{blue}{-196x} & = & \color{red}{196x} +16 \color{blue}{-196x} \color{blue}{+105} \\\Leftrightarrow & -700x-196x& = & 16+105 \\\Leftrightarrow & \color{red}{-896} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-896} & & \\\Leftrightarrow & x = \frac{-121}{896} & & \\ & V = \left\{ \frac{-121}{896} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & -3x+\frac{7}{12} \\\Leftrightarrow & -8x+\frac{8}{5}& = & -3x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-480}{ \color{blue}{60} }x+ \frac{96}{ \color{blue}{60} })& = & (\frac{-180}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -480x \color{red}{+96} & = & \color{red}{-180x} +35 \\\Leftrightarrow & -480x \color{red}{+96} \color{blue}{-96} \color{blue}{+180x} & = & \color{red}{-180x} +35 \color{blue}{+180x} \color{blue}{-96} \\\Leftrightarrow & -480x+180x& = & 35-96 \\\Leftrightarrow & \color{red}{-300} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-300} & & \\\Leftrightarrow & x = \frac{61}{300} & & \\ & V = \left\{ \frac{61}{300} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{21}{8}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{-120x} +48 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{+120x} & = & \color{red}{-120x} +48 \color{blue}{+120x} \color{blue}{-105} \\\Leftrightarrow & -560x+120x& = & 48-105 \\\Leftrightarrow & \color{red}{-440} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-440} & & \\\Leftrightarrow & x = \frac{57}{440} & & \\ & V = \left\{ \frac{57}{440} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{3})& = & -2x+\frac{10}{9} \\\Leftrightarrow & 25x-\frac{20}{3}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-18}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{-60} & = & \color{red}{-18x} +10 \\\Leftrightarrow & 225x \color{red}{-60} \color{blue}{+60} \color{blue}{+18x} & = & \color{red}{-18x} +10 \color{blue}{+18x} \color{blue}{+60} \\\Leftrightarrow & 225x+18x& = & 10+60 \\\Leftrightarrow & \color{red}{243} x& = & 70 \\\Leftrightarrow & x = \frac{70}{243} & & \\ & V = \left\{ \frac{70}{243} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -20x+\frac{20}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+40} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -280x \color{red}{+40} \color{blue}{-40} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{-40} \\\Leftrightarrow & -280x+98x& = & 35-40 \\\Leftrightarrow & \color{red}{-182} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-182} & & \\\Leftrightarrow & x = \frac{5}{182} & & \\ & V = \left\{ \frac{5}{182} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & -5x+\frac{7}{5} \\\Leftrightarrow & -4x+\frac{4}{3}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{-75x} +21 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{+75x} & = & \color{red}{-75x} +21 \color{blue}{+75x} \color{blue}{-20} \\\Leftrightarrow & -60x+75x& = & 21-20 \\\Leftrightarrow & \color{red}{15} x& = & 1 \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+126} & = & \color{red}{385x} +22 \\\Leftrightarrow & -924x \color{red}{+126} \color{blue}{-126} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{-126} \\\Leftrightarrow & -924x-385x& = & 22-126 \\\Leftrightarrow & \color{red}{-1309} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-1309} & & \\\Leftrightarrow & x = \frac{104}{1309} & & \\ & V = \left\{ \frac{104}{1309} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{-48} & = & \color{red}{100x} +45 \\\Leftrightarrow & 160x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & 160x-100x& = & 45+48 \\\Leftrightarrow & \color{red}{60} x& = & 93 \\\Leftrightarrow & x = \frac{93}{60} & & \\\Leftrightarrow & x = \frac{31}{20} & & \\ & V = \left\{ \frac{31}{20} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & 9x+\frac{4}{7} \\\Leftrightarrow & -8x-\frac{12}{11}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-84} & = & \color{red}{693x} +44 \\\Leftrightarrow & -616x \color{red}{-84} \color{blue}{+84} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{+84} \\\Leftrightarrow & -616x-693x& = & 44+84 \\\Leftrightarrow & \color{red}{-1309} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-1309} & & \\\Leftrightarrow & x = \frac{-128}{1309} & & \\ & V = \left\{ \frac{-128}{1309} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{7})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -28x-4& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x- \frac{44}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{-44} & = & \color{red}{-55x} +5 \\\Leftrightarrow & -308x \color{red}{-44} \color{blue}{+44} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{+44} \\\Leftrightarrow & -308x+55x& = & 5+44 \\\Leftrightarrow & \color{red}{-253} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-253} & & \\\Leftrightarrow & x = \frac{-49}{253} & & \\ & V = \left\{ \frac{-49}{253} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{8})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 20x+\frac{15}{8}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{160}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-24}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 160x \color{red}{+15} & = & \color{red}{-24x} +6 \\\Leftrightarrow & 160x \color{red}{+15} \color{blue}{-15} \color{blue}{+24x} & = & \color{red}{-24x} +6 \color{blue}{+24x} \color{blue}{-15} \\\Leftrightarrow & 160x+24x& = & 6-15 \\\Leftrightarrow & \color{red}{184} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{184} & & \\ & V = \left\{ \frac{-9}{184} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -8x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -8x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+132} & = & \color{red}{-440x} +35 \\\Leftrightarrow & -825x \color{red}{+132} \color{blue}{-132} \color{blue}{+440x} & = & \color{red}{-440x} +35 \color{blue}{+440x} \color{blue}{-132} \\\Leftrightarrow & -825x+440x& = & 35-132 \\\Leftrightarrow & \color{red}{-385} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-385} & & \\\Leftrightarrow & x = \frac{97}{385} & & \\ & V = \left\{ \frac{97}{385} \right\} & \\\end{align}\)