Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{441x} +56 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{-90} \\\Leftrightarrow & -630x-441x& = & 56-90 \\\Leftrightarrow & \color{red}{-1071} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-1071} & & \\\Leftrightarrow & x = \frac{2}{63} & & \\ & V = \left\{ \frac{2}{63} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 14x+\frac{28}{3}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{308}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+308} & = & \color{red}{165x} +24 \\\Leftrightarrow & 462x \color{red}{+308} \color{blue}{-308} \color{blue}{-165x} & = & \color{red}{165x} +24 \color{blue}{-165x} \color{blue}{-308} \\\Leftrightarrow & 462x-165x& = & 24-308 \\\Leftrightarrow & \color{red}{297} x& = & -284 \\\Leftrightarrow & x = \frac{-284}{297} & & \\ & V = \left\{ \frac{-284}{297} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{5})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 24x-\frac{24}{5}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-264} & = & \color{red}{275x} +45 \\\Leftrightarrow & 1320x \color{red}{-264} \color{blue}{+264} \color{blue}{-275x} & = & \color{red}{275x} +45 \color{blue}{-275x} \color{blue}{+264} \\\Leftrightarrow & 1320x-275x& = & 45+264 \\\Leftrightarrow & \color{red}{1045} x& = & 309 \\\Leftrightarrow & x = \frac{309}{1045} & & \\ & V = \left\{ \frac{309}{1045} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{3})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{8}{3}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+24} & = & \color{red}{-45x} +8 \\\Leftrightarrow & 108x \color{red}{+24} \color{blue}{-24} \color{blue}{+45x} & = & \color{red}{-45x} +8 \color{blue}{+45x} \color{blue}{-24} \\\Leftrightarrow & 108x+45x& = & 8-24 \\\Leftrightarrow & \color{red}{153} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{153} & & \\ & V = \left\{ \frac{-16}{153} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{3})& = & -6x+\frac{2}{9} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -6x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{-54}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-42} & = & \color{red}{-54x} +2 \\\Leftrightarrow & -252x \color{red}{-42} \color{blue}{+42} \color{blue}{+54x} & = & \color{red}{-54x} +2 \color{blue}{+54x} \color{blue}{+42} \\\Leftrightarrow & -252x+54x& = & 2+42 \\\Leftrightarrow & \color{red}{-198} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-198} & & \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-84} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 924x \color{red}{-84} \color{blue}{+84} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{+84} \\\Leftrightarrow & 924x+385x& = & 110+84 \\\Leftrightarrow & \color{red}{1309} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1309} & & \\ & V = \left\{ \frac{194}{1309} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-132} & = & \color{red}{275x} +10 \\\Leftrightarrow & -495x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -495x-275x& = & 10+132 \\\Leftrightarrow & \color{red}{-770} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-770} & & \\\Leftrightarrow & x = \frac{-71}{385} & & \\ & V = \left\{ \frac{-71}{385} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{3})& = & -9x+\frac{7}{6} \\\Leftrightarrow & 20x+\frac{8}{3}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+16} & = & \color{red}{-54x} +7 \\\Leftrightarrow & 120x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +7 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & 120x+54x& = & 7-16 \\\Leftrightarrow & \color{red}{174} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{174} & & \\\Leftrightarrow & x = \frac{-3}{58} & & \\ & V = \left\{ \frac{-3}{58} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{3}{7})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 24x-\frac{18}{7}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{198}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-198} & = & \color{red}{385x} +63 \\\Leftrightarrow & 1848x \color{red}{-198} \color{blue}{+198} \color{blue}{-385x} & = & \color{red}{385x} +63 \color{blue}{-385x} \color{blue}{+198} \\\Leftrightarrow & 1848x-385x& = & 63+198 \\\Leftrightarrow & \color{red}{1463} x& = & 261 \\\Leftrightarrow & x = \frac{261}{1463} & & \\ & V = \left\{ \frac{261}{1463} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{7})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-176} & = & \color{red}{-231x} +28 \\\Leftrightarrow & -616x \color{red}{-176} \color{blue}{+176} \color{blue}{+231x} & = & \color{red}{-231x} +28 \color{blue}{+231x} \color{blue}{+176} \\\Leftrightarrow & -616x+231x& = & 28+176 \\\Leftrightarrow & \color{red}{-385} x& = & 204 \\\Leftrightarrow & x = \frac{204}{-385} & & \\\Leftrightarrow & x = \frac{-204}{385} & & \\ & V = \left\{ \frac{-204}{385} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{9})& = & -3x+\frac{7}{3} \\\Leftrightarrow & 10x-\frac{20}{9}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{21}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-20} & = & \color{red}{-27x} +21 \\\Leftrightarrow & 90x \color{red}{-20} \color{blue}{+20} \color{blue}{+27x} & = & \color{red}{-27x} +21 \color{blue}{+27x} \color{blue}{+20} \\\Leftrightarrow & 90x+27x& = & 21+20 \\\Leftrightarrow & \color{red}{117} x& = & 41 \\\Leftrightarrow & x = \frac{41}{117} & & \\ & V = \left\{ \frac{41}{117} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-66} & = & \color{red}{385x} +25 \\\Leftrightarrow & -550x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +25 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -550x-385x& = & 25+66 \\\Leftrightarrow & \color{red}{-935} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-935} & & \\\Leftrightarrow & x = \frac{-91}{935} & & \\ & V = \left\{ \frac{-91}{935} \right\} & \\\end{align}\)