Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-2)& = & 3x+\frac{2}{11} \\\Leftrightarrow & -14x+14& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x+ \frac{154}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{+154} & = & \color{red}{33x} +2 \\\Leftrightarrow & -154x \color{red}{+154} \color{blue}{-154} \color{blue}{-33x} & = & \color{red}{33x} +2 \color{blue}{-33x} \color{blue}{-154} \\\Leftrightarrow & -154x-33x& = & 2-154 \\\Leftrightarrow & \color{red}{-187} x& = & -152 \\\Leftrightarrow & x = \frac{-152}{-187} & & \\\Leftrightarrow & x = \frac{152}{187} & & \\ & V = \left\{ \frac{152}{187} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{+36} & = & \color{red}{75x} +20 \\\Leftrightarrow & 360x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 360x-75x& = & 20-36 \\\Leftrightarrow & \color{red}{285} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{285} & & \\ & V = \left\{ \frac{-16}{285} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{2})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{15}{2}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-12}{ \color{blue}{2} }x- \frac{15}{ \color{blue}{2} })& = & (\frac{14}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -12x \color{red}{-15} & = & \color{red}{14x} +3 \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{-14x} & = & \color{red}{14x} +3 \color{blue}{-14x} \color{blue}{+15} \\\Leftrightarrow & -12x-14x& = & 3+15 \\\Leftrightarrow & \color{red}{-26} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-26} & & \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{12})& = & 9x+\frac{7}{12} \\\Leftrightarrow & 28x-\frac{35}{12}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 12 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{-35} & = & \color{red}{108x} +7 \\\Leftrightarrow & 336x \color{red}{-35} \color{blue}{+35} \color{blue}{-108x} & = & \color{red}{108x} +7 \color{blue}{-108x} \color{blue}{+35} \\\Leftrightarrow & 336x-108x& = & 7+35 \\\Leftrightarrow & \color{red}{228} x& = & 42 \\\Leftrightarrow & x = \frac{42}{228} & & \\\Leftrightarrow & x = \frac{7}{38} & & \\ & V = \left\{ \frac{7}{38} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{4})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 10x-\frac{15}{4}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-165} & = & \color{red}{132x} +32 \\\Leftrightarrow & 440x \color{red}{-165} \color{blue}{+165} \color{blue}{-132x} & = & \color{red}{132x} +32 \color{blue}{-132x} \color{blue}{+165} \\\Leftrightarrow & 440x-132x& = & 32+165 \\\Leftrightarrow & \color{red}{308} x& = & 197 \\\Leftrightarrow & x = \frac{197}{308} & & \\ & V = \left\{ \frac{197}{308} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & -4x+\frac{9}{5} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -4x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-30} & = & \color{red}{-140x} +63 \\\Leftrightarrow & -525x \color{red}{-30} \color{blue}{+30} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{+30} \\\Leftrightarrow & -525x+140x& = & 63+30 \\\Leftrightarrow & \color{red}{-385} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-385} & & \\\Leftrightarrow & x = \frac{-93}{385} & & \\ & V = \left\{ \frac{-93}{385} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -18x-\frac{24}{5}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-264} & = & \color{red}{-495x} +30 \\\Leftrightarrow & -990x \color{red}{-264} \color{blue}{+264} \color{blue}{+495x} & = & \color{red}{-495x} +30 \color{blue}{+495x} \color{blue}{+264} \\\Leftrightarrow & -990x+495x& = & 30+264 \\\Leftrightarrow & \color{red}{-495} x& = & 294 \\\Leftrightarrow & x = \frac{294}{-495} & & \\\Leftrightarrow & x = \frac{-98}{165} & & \\ & V = \left\{ \frac{-98}{165} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -14x-\frac{14}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{-154} & = & \color{red}{275x} +50 \\\Leftrightarrow & -770x \color{red}{-154} \color{blue}{+154} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{+154} \\\Leftrightarrow & -770x-275x& = & 50+154 \\\Leftrightarrow & \color{red}{-1045} x& = & 204 \\\Leftrightarrow & x = \frac{204}{-1045} & & \\\Leftrightarrow & x = \frac{-204}{1045} & & \\ & V = \left\{ \frac{-204}{1045} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{6}{5}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-66} & = & \color{red}{495x} +30 \\\Leftrightarrow & -440x \color{red}{-66} \color{blue}{+66} \color{blue}{-495x} & = & \color{red}{495x} +30 \color{blue}{-495x} \color{blue}{+66} \\\Leftrightarrow & -440x-495x& = & 30+66 \\\Leftrightarrow & \color{red}{-935} x& = & 96 \\\Leftrightarrow & x = \frac{96}{-935} & & \\\Leftrightarrow & x = \frac{-96}{935} & & \\ & V = \left\{ \frac{-96}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{-63} & = & \color{red}{-72x} +16 \\\Leftrightarrow & 672x \color{red}{-63} \color{blue}{+63} \color{blue}{+72x} & = & \color{red}{-72x} +16 \color{blue}{+72x} \color{blue}{+63} \\\Leftrightarrow & 672x+72x& = & 16+63 \\\Leftrightarrow & \color{red}{744} x& = & 79 \\\Leftrightarrow & x = \frac{79}{744} & & \\ & V = \left\{ \frac{79}{744} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -8x+\frac{2}{5} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -8x+\frac{2}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-160}{ \color{blue}{20} }x+ \frac{8}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+75} & = & \color{red}{-160x} +8 \\\Leftrightarrow & -300x \color{red}{+75} \color{blue}{-75} \color{blue}{+160x} & = & \color{red}{-160x} +8 \color{blue}{+160x} \color{blue}{-75} \\\Leftrightarrow & -300x+160x& = & 8-75 \\\Leftrightarrow & \color{red}{-140} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-140} & & \\\Leftrightarrow & x = \frac{67}{140} & & \\ & V = \left\{ \frac{67}{140} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{11})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{8}{11}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{-16} & = & \color{red}{198x} +33 \\\Leftrightarrow & -440x \color{red}{-16} \color{blue}{+16} \color{blue}{-198x} & = & \color{red}{198x} +33 \color{blue}{-198x} \color{blue}{+16} \\\Leftrightarrow & -440x-198x& = & 33+16 \\\Leftrightarrow & \color{red}{-638} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-638} & & \\\Leftrightarrow & x = \frac{-49}{638} & & \\ & V = \left\{ \frac{-49}{638} \right\} & \\\end{align}\)