Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-150} & = & \color{red}{-275x} +44 \\\Leftrightarrow & -660x \color{red}{-150} \color{blue}{+150} \color{blue}{+275x} & = & \color{red}{-275x} +44 \color{blue}{+275x} \color{blue}{+150} \\\Leftrightarrow & -660x+275x& = & 44+150 \\\Leftrightarrow & \color{red}{-385} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-385} & & \\\Leftrightarrow & x = \frac{-194}{385} & & \\ & V = \left\{ \frac{-194}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{4})& = & 3x+\frac{9}{11} \\\Leftrightarrow & 20x+\frac{15}{4}& = & 3x+\frac{9}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{880}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{36}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 880x \color{red}{+165} & = & \color{red}{132x} +36 \\\Leftrightarrow & 880x \color{red}{+165} \color{blue}{-165} \color{blue}{-132x} & = & \color{red}{132x} +36 \color{blue}{-132x} \color{blue}{-165} \\\Leftrightarrow & 880x-132x& = & 36-165 \\\Leftrightarrow & \color{red}{748} x& = & -129 \\\Leftrightarrow & x = \frac{-129}{748} & & \\ & V = \left\{ \frac{-129}{748} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{11})& = & 3x+\frac{7}{3} \\\Leftrightarrow & -20x-\frac{16}{11}& = & 3x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-48} & = & \color{red}{99x} +77 \\\Leftrightarrow & -660x \color{red}{-48} \color{blue}{+48} \color{blue}{-99x} & = & \color{red}{99x} +77 \color{blue}{-99x} \color{blue}{+48} \\\Leftrightarrow & -660x-99x& = & 77+48 \\\Leftrightarrow & \color{red}{-759} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-759} & & \\\Leftrightarrow & x = \frac{-125}{759} & & \\ & V = \left\{ \frac{-125}{759} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{3})& = & -3x+\frac{7}{8} \\\Leftrightarrow & -35x-\frac{28}{3}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{224}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-224} & = & \color{red}{-72x} +21 \\\Leftrightarrow & -840x \color{red}{-224} \color{blue}{+224} \color{blue}{+72x} & = & \color{red}{-72x} +21 \color{blue}{+72x} \color{blue}{+224} \\\Leftrightarrow & -840x+72x& = & 21+224 \\\Leftrightarrow & \color{red}{-768} x& = & 245 \\\Leftrightarrow & x = \frac{245}{-768} & & \\\Leftrightarrow & x = \frac{-245}{768} & & \\ & V = \left\{ \frac{-245}{768} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{7})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 4x+\frac{8}{7}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{+16} & = & \color{red}{42x} +63 \\\Leftrightarrow & 56x \color{red}{+16} \color{blue}{-16} \color{blue}{-42x} & = & \color{red}{42x} +63 \color{blue}{-42x} \color{blue}{-16} \\\Leftrightarrow & 56x-42x& = & 63-16 \\\Leftrightarrow & \color{red}{14} x& = & 47 \\\Leftrightarrow & x = \frac{47}{14} & & \\ & V = \left\{ \frac{47}{14} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & -9x+\frac{3}{8} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{896}{ \color{blue}{56} }x+ \frac{128}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 896x \color{red}{+128} & = & \color{red}{-504x} +21 \\\Leftrightarrow & 896x \color{red}{+128} \color{blue}{-128} \color{blue}{+504x} & = & \color{red}{-504x} +21 \color{blue}{+504x} \color{blue}{-128} \\\Leftrightarrow & 896x+504x& = & 21-128 \\\Leftrightarrow & \color{red}{1400} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{1400} & & \\ & V = \left\{ \frac{-107}{1400} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{3})& = & 8x+\frac{3}{8} \\\Leftrightarrow & -21x+\frac{28}{3}& = & 8x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x+ \frac{224}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{+224} & = & \color{red}{192x} +9 \\\Leftrightarrow & -504x \color{red}{+224} \color{blue}{-224} \color{blue}{-192x} & = & \color{red}{192x} +9 \color{blue}{-192x} \color{blue}{-224} \\\Leftrightarrow & -504x-192x& = & 9-224 \\\Leftrightarrow & \color{red}{-696} x& = & -215 \\\Leftrightarrow & x = \frac{-215}{-696} & & \\\Leftrightarrow & x = \frac{215}{696} & & \\ & V = \left\{ \frac{215}{696} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{+48} & = & \color{red}{-70x} +25 \\\Leftrightarrow & 300x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +25 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & 300x+70x& = & 25-48 \\\Leftrightarrow & \color{red}{370} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{370} & & \\ & V = \left\{ \frac{-23}{370} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & -3x+\frac{9}{11} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{36}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{-165} & = & \color{red}{-132x} +36 \\\Leftrightarrow & 1100x \color{red}{-165} \color{blue}{+165} \color{blue}{+132x} & = & \color{red}{-132x} +36 \color{blue}{+132x} \color{blue}{+165} \\\Leftrightarrow & 1100x+132x& = & 36+165 \\\Leftrightarrow & \color{red}{1232} x& = & 201 \\\Leftrightarrow & x = \frac{201}{1232} & & \\ & V = \left\{ \frac{201}{1232} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{7})& = & -8x+\frac{6}{7} \\\Leftrightarrow & -25x-\frac{10}{7}& = & -8x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{-10} & = & \color{red}{-56x} +6 \\\Leftrightarrow & -175x \color{red}{-10} \color{blue}{+10} \color{blue}{+56x} & = & \color{red}{-56x} +6 \color{blue}{+56x} \color{blue}{+10} \\\Leftrightarrow & -175x+56x& = & 6+10 \\\Leftrightarrow & \color{red}{-119} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-119} & & \\\Leftrightarrow & x = \frac{-16}{119} & & \\ & V = \left\{ \frac{-16}{119} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-66} & = & \color{red}{-231x} +70 \\\Leftrightarrow & -616x \color{red}{-66} \color{blue}{+66} \color{blue}{+231x} & = & \color{red}{-231x} +70 \color{blue}{+231x} \color{blue}{+66} \\\Leftrightarrow & -616x+231x& = & 70+66 \\\Leftrightarrow & \color{red}{-385} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-385} & & \\\Leftrightarrow & x = \frac{-136}{385} & & \\ & V = \left\{ \frac{-136}{385} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{16}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{16}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-16} & = & \color{red}{-33x} +6 \\\Leftrightarrow & 88x \color{red}{-16} \color{blue}{+16} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+16} \\\Leftrightarrow & 88x+33x& = & 6+16 \\\Leftrightarrow & \color{red}{121} x& = & 22 \\\Leftrightarrow & x = \frac{22}{121} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)